•; 
IMi 


w,  BLAKEMAN  TAYLOR  &  Co 

BIW  YOEK  and  CHICAGO. 


Vi— -• 


Education  Library 


c 


* 


9 


• 


-A 


PROGRESSIVE 

[INTELLECTUAL  ARITHMETIC; 

ON  THE  INDUCTIVE  PLAN. 

BEING 

A  SEQUEL  TO  THE  PROGRESSIVE  PRIMARY  ARITHMETIC,  CONTAINING 

MANY  ORIGINAL  FORMS  OF  ANALYSIS  APPLICABLE  TO  A 

GREAT  VARIETY   OF  PRACTICAL  QUESTIONS, 

AND    DESIGNED    FOR 

THE    MORE    ADVANCED    CLASSES 

IN 

COMMON     SCHOOLS     AND     ACADEMIES. 

EDITED    BY 

DANIEL  W.  FISH,  A.M. 


IVISON,  BLAKEMAN,  TAYLOR  &  CO., 

PUBLISHERS, 
NEW   YORK'  AND    CHICAGO. 

1878. 


Q 

ROBINSON'S 

M  a  t  h  e  matic al    S  erie s . 

Graded  to  the  wants  of  Primary,  Intermediate,  Grammar, 
Normal,  and  High  Schools,  Academies,  and  Colleges, 


Progressive  Table  Book. 
Progressive  Primary  Arithmetic. 
Progressive  Intellectual  Arithmetic. 
Rudiment*  of  Written  Arithmetic. 

JUNIOK-CLASS  ARITHMKT1C,  Oral  and  Written.    NEW. 
Progressive  Practical  Arithmetic. 
Key  to  Practical  Arithmetic. 
Progressive  Higher  Arithmetic. 
Key  to  Higher  Arithmetic. 
New  Klemeutary  Algebra. 
Key  to  New  Momentary  Algebra. 
New  University  Algebra. 
Key  to  New  University  Algebra. 
New  Geometry  and  Trigonometry.    In  one  vol. 
Geometry,  Plane  and  Solid.     In  separate  vol. 
Trigonometry,  Plane  and  Spherical.    In  separate  vol. 
New  Analytical  Geometry  and  Conic  Sectio 
New  Surveying  and  Navigation.  ^ 

New  Differential  and  Integral  Calculus. 
University  Astronomy—  Descriptive  and  Phys'cal. 

Key  to  Geometry  and  Trigonometry,  Analytical  Geometry  and  Conic  Sec- 
tions, Surveying  and  Navigation. 

Entered,  according  to  Act  of  Congress,  in  the  year  1858,  and  again  in  the  year  1863,  by 
DANIEL    W.    FISH,    A.M., 

In  tne  Clerk's  Office  of  the   District  Court  of  the  United  States,  for  the  Northern 
District  of  New  York. 


'•' 


Q  A  i  * 

RSI 
PREFACE. 


THE  importance,  and  the  practical  benefit  to  be  derived  from  the 
study  of  Intellectual  Arithmetic,  not  only  as  a  preparation  for  busi- 
ness life,  but  as  a  means  of  developing  and  strengthening  the 
thinking  and  reasoning  powers,  and  of  thorough  mental  culture, 
can  not  be  over-estimated.  Not  only  is  it  a  necessary-  study  for 
young  pupils,  but  indispensable  to  the  more  advanced  student,  as 
a  preparation  for  the  prompt  and  accurate  business  man.  And  it 
is  believed  that,  as  a  general  rule,  the  most  critical,  correct,  and 
ready  students  of  mathematics  are  those  who  have  been  most 
thoroughly  drilled  in  intellectual  arithmetic. 

This  work  has  been  prepared  more  especially  for  advanced  classes, 
and  is  designed  for  those  who  have  first  been  well  taught  in  the 
primary  book,  and  for  such  as  are  pursuing  the  study  of  written 
arithmetic,  or  algebra,  and  who  have  never  been  thoroughly  exer- 
cised in  this  branch  of  study. 

Only  a  few  of  the  many  points  of  difference  between  this  and 
other  similar  works,  and  which,  it  is  believed,  renders  this  superior 
to  them,  will  be  referred  to. 

It  is  more  complete,  comprehensive,  and  progressive  In  its  char- 
acter. The  arrangement  and  classification  are  more  strictly  sys- 
tematic, and  in  accordance  with  the  natural  order  of  mathematical 
science.  The  development  of  principles,  and  their  applications, 
are  shown  by  a  more  numerous  selection,  and  greater  variety  of 
appropriate  examples,  progressively  arranged,  commencing  with 
those  that  are  simple  and  easy,  and  advancing  to  those  more  com- 
plex and  difficult. 

At  intervals,  and  especially  in  the  closing  sections  of  each  chap- 
ter, examples  are  given  containing  such  a  combination  of  principles, 
and  forms  of  analysis,  as  to  require  a  knowledge  of  almost  every 
principle  previously  taught,  thus  affording  the  pupil  a  thorough 
review,  as  well  as  requiring  him  to  classify  his  knowledge  of  what 
he  has  been  over. 

One  of  the  most  important,  and,  it  is  thought,  one  of  the  most 
original  and  useful  features  of  this  work,  is  the  full,  concise,  and 
uniform  system  of  ANALYSIS  it  contains,  —  the  result  of  long  expe- 
rience in  the  school-room. 

Particular  attention  is  invited  to  the  subjects  of  Fractions,  Per- 
centage, and  Interest  ;  their  treatment  is  peculiar,  and  adapted  to 
obviate  many  of  the  difficulties,  and  greatly  abbreviate  most  of  the 
operations  in  them. 

M289985 


4  PREFACE. 

The  chapter  of  Miscellaneous  Examples  will  afford  a  valuable 
and  thorough  drill  to  the  advanced  student  of  arithmetic  or  alge- 
bra. They  contain  a  great  variety  of  principles,  and  while  they 
may  be  considered  difficult,  yet  the  full  analysis  given  of  every 
principle,  and  the  selection  of  numbers  so  adapted  to  the  conditions 
of  the  question  as  to  produce  results  free  from  large  and  difficult 
fractions,  will  render  a  mental  solution  of  them  comparatively  easy. 

In  conclusion,  we  may  be  allowed  to  express  the  belie'f,  that 
in  this  work  the  thorough  teacher  will  find  a  desideratum  long 
sought  in  this  department  of  science, — the  means  of  mental  dis- 
cipline and  development  such  as  has  been  furnished  by  uo 
similar  treatise. 

THE  AUTHOR. 


SUGGESTIONS  TO  TEACHERS. 

Pupils  of  nearly  the  same  degree  of  advancement  should  be 
classed  together.  Regular  exercises  should  be  assigned  to  the 
class,  and  sufficient  time  allowed  them  to  thoroughly  examine 
their  lesson  before  being  called  upon  to  recite. 

The  use  of  the  book  at  the  time  of  recitation  should  be  strictly 
prohibited,  except,  perhaps,  in  some  of  the  more  difficult  lessons 
in  the  latter  part  of  the  work. 

Each  example  should  be  read  but  once,  slowly  and  distinctly, 
the  pupils  called  upon  promiscuously,  who  should  arise,  stand 
erect,  repeat  the  example,  and  then  give  the  analysis.  This  will 
secure  close  attention. 

Every  question  should  be  clearly  and  thoroughly  analyzed,  and 
the  pupil  required  to  adhere  strictly  to  the  forms  of  solution  given, 
unless  better  ones  can  be  substituted ;  and  in  no  case  should  he 
be  allowed  to  omit  the  conclusion,  commencing  with  "  Therefore." 

The  class  should  be  encouraged  to  detect  and  correct  errors  in 
/statement  or  analysis,  to  criticise  and  make  proper  inquiries,  all 
of  which  should  be  signaled  by  the  uplifted  hand. 

It  is  suggested  that  the  class  be  occasionally  exercised  upon 
"Ringing  the  Changes,"  as  explained  in  the  Appendix,  and  which 
may  be  applied  to  a  great  number  and  variety  of  examples.  It 
will  not  only  afford  a  valuable  drill,  but  a  pleasant  and  enlivening 
exercise. 


INTELLECTUAL    ARITHMETIC. 


CHAPTER  I. 
ADDITION. 

1.  1.   JAMES  had  1  cent,  and  his  father  gave  him 
1  more  ;  how  many  had  he  then  ? 

2.  If  a  slate  pencil  cost  2  cents,  and  a  steel  pen 
1  cent,  how  many  cents  will  both  cost  ? 

3.  George  spent  2  cents  for  candy,  and  had  2  cents 
left ;  how  many  cents  had  he  at  first  ? 

4.  A  farmer  sold  a  calf  for  3  dollars,  and  a  pig 
for  2  dollars ;  how  many  dollars  did  he  receive  for 
both  ? 

5.  Mary  gave  2  cents  for  some  tape,  and  5  cents 
for  a  thimble  ;  how  many  cents  did  she  give  for  both  ? 

6.  Martin  gave  John  3  apples,  and  kept  4  for  him- 
self; how  many  apples  had  he  at  first  ? 

7.  There  are  4  books  on  one  desk,  and  2  books 
on  another  ;  how  many  books  on  both  desks  ? 

8.  If  a  lemon  cost  3  cents,  and  an  orange  5  cents, 
how  many  cents  do  both  cost  ? 

9.  In  a  Certain  class  there  are  5  girls  and  4  boys ; 
how  many  pupils  in  the  class  ? 

10.  Samuel  had  3  marbles,  and  his  brother  gave 
him  B  more  ;  how  many  did  he  then  have  ? 

11.  Bought  a  barrel  of  apples  for  2  dollars,  and  a 
cord  of  wood  for  4  dollars ;  how  many  dollars  did 
both  cost  *f 

1*  («) 


INTELLECTUAL  ARITHMETIC.  [2. 


1.  !j^4im^  JL  ^re  how  many  ? 

2.  1    jjucU  JU  acejiow  many  ? 

3.  2    and     '1    -are  how  many  ? 

4.  2     and     :)     arejiow  many:' 

5.  2     and     i^arejiow  many?//* 

6.  2     and     ,">     are  how  many  ? 

7.  -J     aint  ~J]ljir£jiow  many  ? 

8.  2    ]an^  <J..^areJy>w  many  ? 

9.  2.  'and     JL«aj£j*ow  many? 

10.  2     ami     9-.  jM-'-C.  how  many  ? 

11.  3__and     3    .qre  how  many  ? 

12. 


13.  gu3ir^Irow  many  ? 

14.  3    ^njLjS-^  are  how  many  ? 

15.  3^and    X  ___  are  how  many? 

16.  3     ancr~8  _  are  how  many  ? 

17.  3     and     0     are  how  many  ? 

18.  3     and  10     are  how  many? 

19.  4    anjL-2     are  how  many  ? 

20.  4     and    j^are  how  many  ? 

21.  r  aiiEIJ:  —  are  how  many  ? 

22.  4_  and    £L—  are  how  many  ? 

23.  4__and  _6     are  how  many  ? 

24.  4     ajiJ^n  nrp  how  many? 

25.  4  ^Hji  j^  are  how  many  ? 

26.  4^jind     9     are  how  many  ? 

27.  4L3!ii^r^are  how  many? 

28.  &^nd^L-  are  how  many  ? 

29.  joT^ni^^  _  are  how  many? 

30.  v/jT   and  t  3^  are  how  many  ? 

31.  ^    and  _jL—  are  how  many? 

32.  ^^  jiudr—  5  __  are  how  many  ? 

33.  _5^  ^and     6     are  how  many  ? 

34.  JL  ^and  ^^1-are  how  many  ? 

35.  ^^JBa.jS^are  how  many  ? 

36.  ^C^nji_^2---a?e  how  many  ? 


3.]  INTELLECTUAL   ARITHMETIC.  7 

3.  1.  A  man  bought  a  calf  for  7  dollars,  and 
sold  it  for  3  dollars  more  than  he  gave  for  it ;  how 
much  did  he  sell  it  for  ? 

2.  Bought  a  barrel  of  cider  for  2  dollars,  and  20 
bushels  of  apples  for  8  dollars  ;   how  many  dollars 
did  the  whole  cost  ? 

3.  If  a  coat  cost  10  dollars,  and  a  pair  of  panta- 
loons 5  dollars,  what  will  be  the  cost  of  both  ? 

4.  A  merchant  bought  4  boxes  of  black  tea,  and 
7  boxes  of  green  tea ;  how  many  boxes  did  he  buy 
of  both  kinds  ? 

5.  A  farmer  sold  5  sheep  to  one  man,  and  9  to 
another  ;  how  many  did  he  sell  to  both  ? 

6.  Ralph  walked  4  miles  and  rode  10  miles  ;  how 
many  miles  did  he  go  ? 

7.  Philip  answered  8  questions  in  geography,  and 
Oliver  5  ;  how  many  questions  did  both  answer  ? 

8.  If  a  quart  of  chestnuts  cost  10  cents,  and  a 
quart  of  walnuts  4  cents,  what  will  be  the  cost  pf 
one  quart  of  both  ? 


9. 

6 

and 

3 

are 

how 

many 

? 

10. 

6 

and 

4 

are 

how 

many 

? 

11. 

6 

and 

5 

are 

how 

many 

? 

12. 

G 

and 

6 

are 

how 

many 

? 

13. 

6 

and 

7 

are 

how 

many 

? 

14. 

6 

and 

8 

are 

how 

many 

? 

15. 

6 

and 

9 

are 

how 

many 

? 

16. 

6 

and 

10 

are 

how 

many 

? 

17. 

7 

and 

4 

are 

how 

many 

? 

18. 

7 

and 

5 

are 

how 

many 

? 

19. 

7 

and 

6 

are 

how 

many 

? 

20. 

7 

and 

7 

are 

how 

many 

? 

21. 

7 

and 

8 

are 

how 

many 

? 

22. 

7 

and 

9 

are 

how 

many 

? 

23. 

rr 
1 

and 

10 

are 

how 

many 

? 

24. 

8 

and 

3 

arc 

how 

many 

? 

INTELLECTUAL   ARITHMETIC.  [4. 

25.  8  and     4  are  how  many  ? 

26.  8  and     5  are  how  many  ? 

27.  8  and     6  are  how  many  ? 

28.  8  and     7  are  how  many  ? 

29.  8  and     8  are  how  many  ? 

30.  8  and     9  are  how  many  ? 

31.  8  and  10  are  how  many  ? 

32.  9  and     4  are  how  many  ? 

33.  9  and     5  are  how  many  ? 

34.  9  and     6  are  how  many? 

35.  9  and     7  are  how  many  ? 

36.  9  and     8  are  how  many  ? 

37.  9  and     9  are  how  many  ? 
88.     9  and  10  are  how  many  ? 

39.  10  and     4  are  how  many  ? 

40.  10  and     5  are  how  many  ? 

41.  10  and     6  are  how  many  ? 


4.  1.  Eli  paid  9  shillings  for  a  pair  of  skates, 
and  6  shillings  for  a  cap ;  how  many  shillings  did  he 
pay  for  both  ? 

ANALYSIS.  Since  Eli  paid  9  shillings  for  a  pair  of 
skates,  and  6  shillings  for  a  cap,  he  paid  for  both,  the 
sum  of  9  shillings  -and  6  shillings.  The  sum  of  9  shil- 
lings and  6  shillings  is  15  shillings.  Therefore,  he  paid 
J  5  shillings  for  both. 

2.  A  farmer  sold  some  oats  for  7  dollars,  and  a 
ton  of  hay  for  9  dollars  ;  how  many  dollars  did  ho 
receive  for  both  ? 

3.  Paid  8  cents  for  some  raisins,  and  6  cents  for 
some  cloves ;  how  many  cents  did  both  cost  ? 

4.  Nancy  is  10  years  old;,  how  old  will   she  be 
5  years  from  this  time  ? 

5.  A  lady  paid  7  dollars  for  a  shawl,  and  6  dol- 
lars for  a  dress  :  what  was  the  cost  of  both  ? 


S.j  INTELLECTUAL   ARITHMETIC.  9 

6.  There  are  9  boys  in  one  class,  and  7  in  anoth- 
er ;  how  many  in  both  classes  ? 

7.  Margaret  has  8  flower  pots  in  one  room,  and  5 
in  another ;  how  many  has  she  in  the  two  rooms  ? 

8.  If  you  read  10  pages  to-day,  and  7  pages  to- 
morrow, how  many  will  you  read  in  both  days  ? 

9.  If  a  firkin  of  butter  is  worth  9  dollars,  and 
two  cords  of  wood  are  worth  8  dollars,  what  are  both 
worth  ? 

10.  Myron  has  6  young  rabbits  and  4  old  ones ; 
how  many  rabbits  has  he  ? 

11.  There  are  10  biids  sitting  on  one  limb,  and 
9  on  another ;  how  many  birds  on  both  limbs  ? 

12.  A  boy,  having  some  peaches  given  him,  put  8 
into  his  hat,  and  7  into  his  pockets ;    how   many 
peaches  were  given  him  ? 

13.  Edwin  found  6  ripe  pears  under  one  tree,  and 
8  under  another ;  how  many  pears  did  he  find  under 
both  trees  ? 

14.  In  one  yard  are  5  cows,  and  in  another  7 ; 
liow  many  cows  in  both  yards  ? 

15.  If  you  work  8  examples  in  arithmetic  to-day, 
and  8  more  to-morrow,  how    many   will   you   work 
in  both  days  ? 

16.  Robert  gave  8  nuts  to  Henry,  and  kept  9  ;  how 
many  nuts  had  he  at  first  ? 


1.  7  and  4  are  how  many  ? 

2.  9  and  7  are  how  many  ? 

3.  6  and  7  are  how  many  ? 

4.  5  and  9  are  how  many  ? 

5.  8  and  7  are  how  many  ? 

6.  10  and  6  are  how  many  ? 

7.  9  and  6  are  how  many  ? 

8.  8  and  8  are  how  many  ? 


10  INTELLECTUAL   ARITHMETIC.                      [5. 

9.  6  and     8  are  how  many  ? 

10.  7  and     9  are  how  many  ? 

11.  8  and  10  are  how  many  ? 

12.  11  and     5  are  how  many  ? 

13.  13  and     7  are  how  many? 

14.  14  and     6  are  how  many? 

15.  12  and     4  are  how  many? 

16.  15  and     8  are  how  many? 

17.  9  and  12  are  how  many  ? 

18.  16  and     8  are  how  many? 

19.  17  and  10  are  how  many? 
V20.  15  and  11  are  how  many  ? 
21.  13  and  12  are  how  many? 


t 

^22. 


22.  How  many  are  2  and  2  ?  12  and  2  ?  22  and 

2  ?  32  and  2  ?  42  and  2  ?  52  and  2  ?  62  and  2  ? 

72  and  2  ?  82  and  2  ?  92  and  2  ? 

23.  How  many  are  3  and  3  ?  13  and  3  ?  23  and 

3  ?  33  and  3  ?  43  and  3  ?  53  and  3  ?  63  and  3  ? 

73  and  3  ?  83  and  3  ?  93  and  3  ? 

24.  How  many  arc  4  and  4  ?  14  and  4?  24  and 

4  ?  34  and  4  ?  44  and  4  ?  54  and  4  ?  64  and  4  ? 

74  and  4?  84  and  4?  94  and  4? 

25.  How  many  are  5  and  5  ?  15  and  5  ?  25  and 

5  ?  35  and  5  ?  *  45  and  5  ?  55  and  5  ?  65  and  5  ? 

75  and  5  ?  85  and  5  ?  95  and  5  ? 

26.  How  many  are  6  and  6  ?  16  and  6  ?  26  and 

6  ?  36  and  6  ?  46  and  6  ?  56  and  6  ?  66  and  6  ? 

76  and  6  ?  86  and  6  ?  96  and  6  ? 

27.  How  many  are  7  and  7  ?  17  and  7  ?  27  and 
7?  37  and  7?  47  and  7  ?  57  and  7  ?  67  and  7? 

77  and  7  ?  87  and  7  ?  97  and  7  ? 

28.  How  many  are  8  and  8  ?  18  and  8  ?  28  and 
8  ?  38  and  8  ?  "  48  and  8  ?  58  and  8  ?  68  and  8  ? 

78  and  8  ?  88  and  8  ?  98  and  8  ? 

29.  How  many  are  9  and  9  ?  19  and  9  ?  29  and 


O.]       INTP:LLECTUAL  ARITHMETIC.        H 

30.  How  many  are  8  and  7  ?  18  and  7  ?  28  and 

7  ?  38  and  7  ?  48  and  7  ?  58  and  7  ?  68  and  7  ? 

78  and  7  ?  88  and  7  ?  98  and  7  ? 

31.  How  many  are  10  and  10  ?  20  and  10  ?  30 
and  10  ?  40  and  10  ?  50  and  10  ?  60  and  10  ?  70 
and  10  ?  80  and  10  ?  90  and  10  ? 

32.  How  many  are  4  and  8  ?  14  and  8  ?  24  and 

8  ?  34  and  8  ?  44  and  8  ?  54  and  8  ?  64  and  8  ? 
74  and  8  ?  84  and  8  ?  94  and  8  ? 

33.  How  many  are  6  and  5  ?  16  and  5  ?  26  and 
5  ?  36  and  5  ?  46  and  5  ?  56  and  5  ?  66  and  5  ? 
76  and  5  ?  86  and  5  ?  96  and  5  ? 

34.  How  many  are  11  and  9  ?  21  and  9  ?  31  and 

9  ?  41  and  9  ?  51  arid  9  ?  61  and  9  ?  71  and  9  ? 
81  and  9  ?  91  and  9  ? 

35.  How  many  are  9  and  7  ?  19  and  7  ?  29  and 

7  ?  39  and  7  ?  49  and  7  ?  59  and  7  ?  69  and  7  ? 

79  and  7  ?  89  and  7  ?  99  and  7  ? 

36.  How  many  are  4  and  8  ?  14  and  8  ?  24  and 

8  ?  34  and  8  ?  44  and  8  ?  54  and  8  ?  64  and  8  ? 
74  and  8  ?  84  and  8  ?  94  and  8  ? 

37.  How  many  are  3  and  10  ?   13  and  10  ?  23 
and  10  ?  33  and  10  ?  43  and  10  ?  53  and  10  ? 
63  and  10  ?  73  and  10  ?  83  and  10  ?  93  and  10  ? 


6.  Addition  is  the  process  of  uniting  several  numbers 
of  the  same  kind  into  one  equivalent  number.  The  result 
is  called  the  Sam  or  Amount.  The  sign  of  addition  is 
written  thus,  +,  and  is  called  plus.  When  placed  between 
two  numbers  or  quantities,  it  shows  that  they  are  to  be 
added  together.  Thus,  5  +  3  +  2  signifies  that  5  and  3 
and  2  are  to  be  added  together,  and  is  read  five,  plus  three, 
plus  two. 

The  sign  of  equality  is  written  thus,  :=.  When  placed 
between  two  numbers  or  quantities,  it  signifies  that  the 
latter  is  equal  to  the  former. 


12  INTELLECTUAL   ARITHMETIC.  [6. 

1.  6  +     4  +     5  are  how  many? 

2.  9  +     7  +     3  are  how  many? 

3.  10  +     6   4-     4  are  how  many? 

4.  13  -f-     8  +     6  are  how  many? 

5.  12  +  10  +     9  are  llow  many? 

6.  11  4"     6' 4" -7  are  how  many? 

7.  8  -f  10  +     7  +  6     are  now  many? 

8.  34  -jr  ~>}  are  uow  many  ? 

ANALYSIS.  As  many  as  the  sum  of  34  and  25  ;  34 
is  composed  of  3  tens  and  4  units,  and  25  0/*  2  tens  and  5 
units ;  3  te?is  and  2  fc>*s  are  5  tos,  or  50,  arca7  4  w 
and  5  im/te  are  9  units,  which  added  to  50  makes 
Therefore  34  +  25  are  59. 


9.     46 

10.  35 

11.  40 


31  are  how  many? 

52  are  how  many  ? 

JLI.  <±v  -t-  80  -f-     6  are  how  many  ? 

12.  19  4"  12  4~     8  are  how  many  ? 

13.  60  4~  72  4-     4  are  how  many? 

14.  48  +  80  +  10  are  how  many  ? 

15.  13  4-  25  4-     7  are  how  many  ? 

16.  29  4-  24  4-  30  are  how  many? 

17.  64  4-  40  4-     9  ai*e  how  many? 

18.  29  +  17  +  12  are  how  many? 

19.  7   4~  37   4-  26  are  how  many  ?  ^ 

20.  14  4~  39  4~     4  are  how  many  ? 

21.  48  4~  31  4~     9  are  h°w  many? 

22.  56  4"  41  +  10  are  how  many  ? 

23.  75  4-  60  4-  20  are  how  many? 

24.  16  4-  19  4~  28  are  how  many? 

25.  43  +  37  +  15  are  how  many? 

26.  84  +  75  4-  20  are  how  many? 

27.  68  4-  52  4-  45  are  how  many? 

28.  35  +  77  4-  51  are  how  many  ? 

29.  80  +  95  +   12  are  how  many? 

30.  42   4-   ?&  4-17   +  9     are  how  many? 


7.]  INTELLECTUAL    ARITHMETIC.  13 

7.  1.  A  man  gave  12  dollars  for  some  corn,  8 
dollars  for  a  ton  of  hay,  and  6  dollars  for  a  barrel  of 
flour ;  how  much  did  he  pay  for  all  ? 

ANALYSIS.  He  p^v^  the  sum  of  12  dollars,  8  dollars, 
and  §  dollars;  12  and  8  are  20,  and  6  are  26  dollars. 
Therefore,  fyc. 

2.  Emily  paid  12  shillings  for  a  dress,  10  shillings 
for   a   pair   of  shoes,  and  6  shillings  for  a  pair  of 
gloves  ;  what  was  the  cost  of  the  whole  ? 

3.  A  drover  had  15  horses  in  one  pasture,  13  in 
another,  and  9  in  another  ;  how  many  horses  had  he  ? 

4.  James  has  10  cents,  Henry  has  7,  and  John 
has  5  ;  how  many  cents  have  the  three  boys  ? 

5.  Bought  a   pound  of  candles  for  14  cents,  a 
pound  of  coffee  for  12  cents,  and  a  bar  of  soap  for 

9  cents  ;  what  was  the  cost  of  the  whole  ? 

6.  In  a  shop  are  7  men,  9  boys,  and  6  girls  at 
work  ;  how  many  persons  at  work  in  the  shop  ? 

7.  A  lady  sold  10  pounds  of  butter  at  one  time, 
12  pounds    at   another,  and  8  pounds  at  another; 
how  many  pounds  did  she  sell  in  all  ? 

8.  William   bought   an  arithmetic  for   15   cents, 
a  quire  of  paper  for  12  cents,  and  a  bottle  of  ink  for 
6  cents  ;  what  was  the  cost  of  the  whole  ? 

9.  Peter,  Dexter,  and  Irwin  gave  some  money  to 
a  beggar  ;  Peter  gave  him  10  cents,  Dexter  11  cents, 
and  Irwin  13  cents  ;  how  many  cents  did  they  all 
give  him  ? 

10.  In  a  certain  school  there  are  18  girls  and  £4 
boys  ;  how  many  pupils  in  the  school  ? 

11.  A  man  bought  a  sleigh  for  20  dollars,  paid 

10  dollars  for  repairing  it,  and  6  dollars  for  paint- 
ing it ;  what  did  it  cost  him  ? 

12.  Morgan  earned  25  cents  one  day,  and  32  the 
next ;  how  much  did  he  earn  in  both  days  ? 


14  INTELLECTUAL   ARITHMETIC.  [7. 

13.  A  farmer  sold  a  cow  for  22  dollars,  a  ton  of 
hay  for  11  dollars,  and  a  calf  for  7  dollars ;  what 
did  he  receive  for  all  ? 

14.  A   traveler   walked   3C    miles   one    day,   26 
miles  the  next,  and  21  miles  the  next ;  how  many 
miles  did  he  travel  in  the  three  days  ? 

15.  One  day  Sarah  wrote  18  lines,  Maria  16,  and 
Carrie  15  ;  how  many  lines  did  they  all  write  ? 

10.  A  man  gave  60  dollars  for  a  horse,  23  dollars 
for  a  saddle,  and  9  dollars  for  a  bridle  ;  what  was  the 
cost  of  the  whole  ? 

17.  Rollin  received  36  new  cents  on  his  birthday, 
34  on  Christmas  day,  and  27  on  New  Year's  day ; 
how  many  cents  did  he  receive  ? 

18.  A  man  bought  a  piece  of  land  for  56  dollars, 
and  paid  25  dollars  for  fencing  it ;   for  how  much 
must  he  sell  it  to  gain  15  dollars  ? 

19.  Amasa,  going  into  the  orchard,  found  12  ripe 
apples  under  one  tree,  15  under  another,  11  under 
another,  and  9  under  another;  how. many  apples  did 
he  find  under  the  four  trees  ? 

20.  A  grocer  bougfit  some  hams  for  20  dollars, 
some  oats  for  19  dollars,  some  fowls  for  16  dollars, 
and  five    barrels    of  apples    for   10    dollars ;    what 
did  he  pay  for  all  ? 

21.  A  miller  shipped   by  railroad    28  barrels  of 
flour  at  one  time,  37  at  another,  and  40  at  another ; 
how  many  barrels  did  he  ship  ? 

22.  If  Lucian  gave  45  cents  for  a  penknife,  15 
cents  for  some  paper,  12  cents  for  a  folder,  and  7 
cents  for  some  wafers,  what  did  the  whole  cost  him  ? 

23.  A  drover  bought  26  sheep  of  one  man,  30  of 
another,  37  of  another,  and  40  of  another ;  how  many 
sheep  did  he  purchase  ? 

24.  Bought  a  horse  for  75  dollars,  and  sold  him 
so  as  to  gain  25  dollars  ;  how  much  did  I  receive  for 
him? 


7.]  INTELLECTUAL   ARITHMETIC.  15 

25.  A  lady  went  shopping,  and  bought  a  silk  dress, 
for  22  dollars,  a  muff  for  16  dollars,  a  shawl  for  14 
dollars,  and  had  7  dollars  left ;   how  much  money 
had  she  at  first  ? 

26.  Peleg  bought  a  knife  for  35  cents  ;  he  gave 
the  knife  and  12  cents  for  a  sled,  which  he  sold  so  as 
to  gain  10  cents  on   the   cost;   how  much  did  he 
receive  for  the  sled  ? 

27.  In  a  certain  orchard  are  31  apple  trees,  27 
peach  trees,  and  19  pear  trees ;  how  many  trees  in 
the  orchard  ? 

28.  A  farmer  raised  54  bushels  of  wheat,  66  bush- 
els of  oats,  and  40  bushels  of  corn  ;  how  many  bush- 
els of  grain  did  he  raise  ? 

29.  If  it  be  62  feet  from  the  ground  to  the  belfry 
of  a  church,  and  76  feet  from  the  belfry  to  the  top 
of  the  steeple,  how  high  is  the  top  of  the  steeple  from 
the  ground  ? 

30.  In  March  are  31  days,  in  April  30,  in  May  31 ; 
how  many  days  in  those  three  months  ? 

31.  If  a  farm  contain  83  acres  of  cleared    land 
and  25  acres  of  wood  land,  how  many  acres  are  in 
the  whole  farm  ? 

32.  The  distance  from  Boston  to  Worcester  is  44 
miles,  from  Worcester  to  Warren  29  miles,  and  from 
Warren  to  Springfield  25  miles ;  how  many  miles 
from  Boston  to  Springfield  ? 

33.  Batavia  is  37  miles  west  from  Rochester,  and 
31  miles  east  from  Buffalo  by  railroad ;  what  is  the 
distance  from  Rochester  to  Buffalo  ? 

34.  A  tailor  bought  three  pieces  of  cloth,  the  first 
containing  29  yards,  the  second  26  yards,  and  the 
third  25  yards  ;  how  many  yards  did  the  three  pieces 
contain  ? 

35.  A  mechanic  sold  a  carriage  for  15  dollars,  and 
a  sleigh  for  48  dollars  ;  what  did  he  receive  for  both  ? 


16  INTELLECTUAL   ARITHMETIC.  [8. 

36.  A  soldier  was  33  years  of  age  when  ho  en- 
gaged  in  the  battle  of  New  Orleans ;  what  was  his 
age  44  years  after  ? 

37.  A  farmer  received  29  dollars  for  some  pork, 
18  dollars  for  some  hay,  15  dollars  for  some  oats,  and 
12  dollars  for  four  cords  of  wood ;  how  many  dollars 
did  he  receive  for  the  whole  ? 

38.  Thomas  hoed  13  rows  of  corn,  Lyman  16  rows, 
Cyrus  14  rows,   and  Warren  10  rows;  how  many 
rows  did  they  all  hoe  ? 

39.  A  gentleman   gave  80  dollars  for  a  coat,  7 
dollars  for  a  vest,  11  dollars  for  a  pair  of  pantaloons, 
and  5  dollars  for  a  hat ;  what  was  the  cost  of  all  ? 

40.  Paid  60  dollars  for  a  carriage,  which,  with  25 
dollars,  I  gave  for  a  horse ;  paid  12  dollars  for  his 
keeping,  and  then  sold  him  for  20  dollars  more  than 
he  cost  me ;  for  how  much  did  I  sell  him  ? 

41.  A  man  deposited  40  dollars  in  a  bank,  which 
was  15  dollars  less  than  his  neighbor  deposited  at 
the  same  time  ;  how  much  did  both  deposit  ? 


CHAPTER   II. 
SUBTRACTION. 

8.  1.  JAMES,  having  5  cents,  gave  2  cents  for  a 
pencil ;  how  many  cents  had  he  left  ? 

ANALYSIS.  Since  James  had  5  cents,  and  gave  2  cents 
for  a  pencil,  he  had  left  the .  difference  between  5  cents 
and  2  cents.  The  difference  betitfeen  5  cents  and  2  cents, 
is  3  cents.  Therefore,  he  had  3  cents  left. 

2.  Mary  had  3  peaches,  and  ate  1  of  them ;  how 
many  had  she  left  ? 

3.  Ella  had  6  pinks,  and  gave  her  sister  2  ;  how 
many  had  she  left  ? 


8.J  INTELLECTUAL    ARITHMETIC.  17 

4.  On  a  rose  bush  were  7  roses,  and  Eliza  picked 
3  of  them ;  how  many  were  left  ? 

5.  A  man  bought  10  sheep  and  sold  5  of  them ; 
how  many  had  he  left  ? 

6.  A  bad  boy  robbed  a  bird's  nest  of  7  eggs,  and 
broke  4  of  them  ;  how  many  remained  unbroken  ? 

7.  If  there  are  8  pigs  in  a  pen,  and  five  of  them 
get  out,  how  many  remain  ? 

8.  If  a  merchant  have  12  barrels  of  flour,  and 
lie  sell  7  of  them,  how  many  barrels  will  he  have 
left? 

9.  Margaret  is  11  years  old,  and  Julia  4  years 
younger  ;  what  is  Julia's  age  ? 

10.  Stephen  had  9  marbles,  and  lost  3  of  them  ; 
how  many  had  he  left  ? 

11.  A  man,  earning  10  dollars  a  week,  spends  6 
dollars   for  provisions ;    how  many  dollars    has  he 
left? 

12.  Giles  borrowed  12  dollars,  and  paid  7  dollars 
of  it ;  how  much  of  it  remained  unpaid  ? 

13.  5     less     3     are  how  many? 

14.  9     less     2     are  how  many? 

15.  7     less     4     are  how  many? 

16.  11     less     3     are  how  many? 

17.  8     less     2     are  how  many? 

18.  6     less     4     are  how  many? 

19.  10     less     6     are  how  many? 

20.  7     less     5     are  how  many? 

21.  14     less     8     are  how  many? 

22.  12     less     7     are  how  many? 

23.  9     less     8     are  how  many? 

24.  15  less     9  are  how  many? 

25.  20  less     6  are  how  many? 

26.  23  less  10  are  how  many? 

27.  18  less     4  are  how  many? 
2 


18  INTELLECTUAL  ARITHMETIC.  [9. 

28.  11     from     14     leaves  how  many? 

29.  9     from     12     leaves  how  many  ? 

30.  7     from     16     leaves  how  many? 
81.  12     from     20     leaves  how  many? 

32.  10     from     17     leaves  how  many? 

33.  8     from     18     leaves  how  many  ? 

34.  6     from     15     leaves  how  many  ? 

35.  11     from     21     leaves  how  many  ? 

86.  Take     5  from  12,  and  how  many  remain  ? 

37.  Take  10  from  19,  and  how  many  remain  ? 

38.  Take     7  from  11,  and  how  many  remain? 

39.  Take     9  from  13,  and  how  many  remain  ? 

40.  Take  12  from  23,  and  how  many  remain  ? 

41.  What  is  the  difference  between  14  and     6? 

42.  What  is  the  difference  between  20  and     8  ? 

43.  What  is  the  difference  between  19  and  15? 

44.  What  is  the  difference  between  11  and  22? 

45.  What  is  the  difference  between  17  and     6  ? 

46.  What  is  the  difference  between  25  and     9  ? 


9.  Subtraction  is  the  process  of  finding  the  difference 
between  two  numbers  ;  the  result  is  called  the  Difference  or 
Remainder.  The  sign  of  subtraction  is  written  thus,  — , 
and  is  read  minus.  Placed  between  two  numbers,  or  quan- 
tities, it  shows  that  the  one  after  it  is  to  be  taken  from  the 
one  before  it.  9  —  5  shows  that  5  is  to  be  subtracted  from 
9,  and  is  read  nine  minus  jive. 

1.  How  many  are  10  —  6  ? 

2.  How  many  are     9  —  4  ? 

3.  How  many  are  12  —  7  ? 

4.  How  many  are  15  —  9? 

5.  How  many  are  20  —  8? 

6.  How  many  are  18  —  5  ? 

7.  How  many  are  17  —  3  ? 

8.  How  many  are  21  —  9? 


ID.]  INTELLECTUAL   ARITHMETIC.  19 

9.     How  many  are  16  —     7  ? 

10.  How  many  are  19  —     9? 

11.  How  many  are  21  —  12? 

12.  How  many  are  17  —  10? 

13.  How  many  are  18  —    9? 

14.  How  many  are  20  —  11? 

15.  How  many  are  25  —  10? 

16.  How  many  are  32  —  12? 

17.  How  many  are  46  —  10? 

18.  How  many  are  57  —  34? 

ANALYSIS.  57  is  equal  to  5  tens  and  7  units,  and  34  is 
equal  to  3  tens  and  4  units  ;  3  tens  from  5  tens  leave  2  tens, 
or  20,  and  4  units  from  7  units  leave  3  units,  which  added 
to  20  make  23.  Therefore,  57  —  34  =  23. 

19.  39  —  27  are  how  many  ? 

20.  43  —  32  are  how  many  ? 

21.  29  —  17  are  how  many  ? 

22.  54  —  21  are  how  many  ? 

23.  67  —  45  are  how  many  ? 

24.  75  —  25  are  how  many  ? 

25.  89  —  74  are  how  many  ? 

26.  39  —  19  are  how  many  ? 

27.  41  —  30  are  how  many? 

28.  96  —  81  are  how  many? 


1O.     1.   If  you  have  12  turkeys,  and  sell  9   of 
them,  how  many  will  you  have  left? 

2.  A  grocer  had  10  boxes  of  lemons,  and  sold  6 
boxes  ;  how  many  boxes  had  he  left  ? 

3.  There  are   20  men  and  8  boys  at  work  in  a 
bookbindery ;    how  many  more  men  than  boys  are 
there  ? 

4.  From  a  cistern  holding  36  barrels  of  water,  12 
barrels  leaked  out ;  how  many  barrels  remained  ? 


20  INTELLECTUAL   ARITHMETIC.  [1C. 

5.  A  man,  having  25  dollars  due  him,  received  a 
ton  of  hay  worth  11  dollars,  and  the  remainder  in 
money  ;  how  much  money  did  he  receive  ? 

6.  There  are  46  trees  in  an  orchard ;  85  of  them 
are  apple  trees  and  the  remainder  peach  trees ;  how 
many  are  peach  trees  ? 

7.  From  a  piece  of  broadcloth  containing  27  yards, 
15  yards  were  cut ;  how  many  yards  remained  ? 

8.  A  jeweler  bought  a  watch  for  60  dollars,  and 
sold   it  again   for   75    dollars ;    how   much   did  he 
gain  ? 

9.  The  whole  number   of  pupils   registered  in  a 
certain  school  is  87,  and  but  65  are  in  attendance ; 
how  many  are  absent  ? 

10.  Charles  has  48  cents,  and  buys  a  slate  for  16 
cents  ;  how  many  cents  has  he  left  ? 

11.  There   are  36  wild  ducks  in  a  flock,  and  a 
huntsman  fires  at  them  and  kills  13 ;  how  many  are 
left? 

12.  A  farmer  sold  a  cow  for  22  dollars  that  cost 
him  30  dollars ;  how  much  did  he  lose  by  the  bar- 
gain ? 

13.  A  grocer  bought  a  quantity  of  sugar  for  39 
dollars,  and  sold  it  for  50  dollars  ;  how  much  did  he 
gain  ? 

14.  In  a  school  are  2?  boys  and  35  girls ;  ho\* 
many  more  girls  than  boys  ? 

15.  The  distance  from  Cincinnati  to  Miamisburg 
by  railroad  is  49  miles,  and  to  Dayton  60  miles; 
what  is  the  distance  from  Miamisburg  to  Dayton  ? 

16.  In  a  warm  day  the  thermometer  indicated  85 
degrees ;    how  many   degrees  was   that   above   th^ 
freezing  point,  which  is  32  degrees  ? 

17.  A  man  died  at  the  age  of  77  years,  having 
been  married  49  years ;  what  was  his  age  when  he 
married  ? 


11.]  INTELLECTUAL   ARITHMETIC.  21 

11.    1.  4  and    7  and    9,  less    8,  are  how  many  ? 

2.  9  and  12  and    6,  less    7,  are  how  many  ? 

3.  14  and  10  and  12,  less  24,  are  how  many  ? 

4.  20  and  16  and    5,  less  14,  are  how  many  ? 

5.  44  and  20  and  10,  less  50,  are  how  many  ? 

6.  27  and  15  and  12,  less  30,  are  how  many  ? 

7.  How  many  are    9  +  12  +  15  —  25  ? 

8.  How  many  are  26  +  15  +     7  —  18  ? 

9.  How  many  are  40  +  10  +     8  —  20  ? 

10.  How  much  less  than    64,  is  25  +  20  ? 

11.  How  much  less  than    56,  is  28  +  16  ? 

12.  How  much  less  than  100,  is  46  +  34  ? 

13.  How  many  are  16  +  12   +  9  +  5  —  32 
i    8? 

14.'  How  many  are  33  +  28  +    9  —  30  -f  15  ? 

15.  How  many  are  84  +  26  +  15  —  70  +  25  ? 

16.  A  man,  having  30  dollars,  paid  15  dollars  for 
a  coat,  5  dollars  for  a  vest,  and  4  dollars  for  a  hat ; 
how  much  had  he  left  ? 

ANALYSIS.  He  had  left  the  difference  between  30  dollars 
and  the  sum  of  15  -j-  5  -f-  4  dollars  ;  15  dollars  and  5 
dollars  are  20  dollars,  and  4  dollars  are  24  dollars,  and  30 
dollars  less  24  dollars  are  6  dollars.  Therefore,  fyc. 

17.  Ellen  had  15  pi^ks,  and  she  gave  6  to  Mary 
and  4  to  Jane  ;  how  many  had  she  left  ? 

18.  A  woman,  having  25  pounds  of  butter,  sold  15 
pounds  at  one  time,  and  10  pounds  at  another ;  how 
many  pounds  had  she  left  ? 

19.  Amasa  has  45  cents  in  three  boxes;  in  the 
first  are  15  cents,  in  the  second  19  cents ;  how  many 
cents  are  in  the  third  box  ? 

20.  A  boy  found  8  apples  under  one  tree.  10  under 
another,  and  6  under  another ;  he  ate  3,  gave  away 
7,  and  carried  the  remainder  home;  how  many  did 
he  take  home  ? 


22  INTELLECTUAL   ARITHMETIC.  [11. 

21.  Martin,  having  27  marbles,  gave  12  to  Albert, 
and  lost  5  ;  how  many  had  he  left  ? 

22.  Reuben  had  16  cents ;  Charles  gave  him  10, 
Elisha  gave  him  9,  and  Henry  gave  him  enough  to 
make  his  number  42 ;  how  many  cents  did  Henry 
give  him  ? 

23.  A  merchant  bought  a  hogshead  of  sugar  for 
50  dollars  ;  he  paid  6  dollars  for  freight  and  customs, 
and  sold  the  whole  for  75  dollars ;  how  much  did  he 
gain  ? 

24.  A  man  bought  a  watch  for  40  dollars,  a  chain 
for  15  dollars,  and  a  key  lor  3  dollars,  and  he  sold 
the  whole  for  50  dollars  ;  how  much  did  he  lose  by 
the  bargain  ? 

25.  Sarah  bought  a  comb  for  12  cents,  some  rib- 
bon for  16  cents,  a  thimble  for  10  cents,  and  some 
thread  for  6  cents ;  how  much  had  she  left  of  fifty 
cents,  after  paying  for  these  articles  ? 

26.  A  drover  bought  9  sheep  of  one  man,  12  of 
another,  and  15  of  another  ;  he  afterwards  sold  8 
and  butchered  5  ;  how  many  had  he  left  ? 

27.  From  a  piece  of  calico  containing  26  yards 
Jane  bought  a  dress  of  9  yards,  and  Josephine  an- 
other of  10  yards  ;  how  many  yards  were  left  in  the 
piece  ? 

28.  Richard,  receiving  45  dollars  for  labor,  paid 
20  dollars  for  a  cow,  7  dollars  for  a  barrel  of  flour, 
and  9  dollars  for  three  cords  of  wood;  how  many 
dollars  had  he  left  ? 

29.  Four  men  bought  a  horse  for  80  dollars ;  the 
first  gave  25  dollars,  the  second  20  dollars,  and  the 
third  18  dollars ;  how  much  did  the  fourth  give  ? 

30.  A  boy  had  12  marbles  ;  another  boy  gave  him 
10  more,  another  9.  and  another  enough  more  to 
make  his  number  40  ;  how  many  did  the  last  boy 
give  him  ? 


11.]  INTELLECTUAL   ARITHMETIC.  23 

31.  A  man  traveled  22  miles  one  day,  and  26 
miles  the  second  day,  and  on  the  third  day  he  trav- 
eled 30  miles  on  his  return ;  how  many  miles  was  he 
from  the  place  from  which  he  first  started  ? 

32.  George  sold  two  dozen  eggs  for  20  cents,  one 
Imshel  of  apples  for  37  cents,  and  received  a  pair  of 
skates  worth  75  cents  ;  how  much  did  he  still  owe 
for  his  skates  ? 

33.  A  man  owed  his  grocer  18  dollars,  his  tailor 
20  dollars,  and  a  merchant  25  dollars ;  he  paid  the 
grocer  10  dollars,   the  tailor   12    dollars,   and   the 
merchant  15  dollars  ;  how  much  did  he  still  owe 
them  all  ? 

34.  Bought  a  horse  for  90  dollars,  a  cutter  for  40 
dollars,  and  a  harness  for  20  dollars,  and  then  sold 
the  whole  for  50  dollars  more  than  the  horse  cost 
me ;   did  I  gain  or  lose  by  the  bargain,  and  how 
much  ? 

35.  A  lady  bought  a  new  bonnet  for  7  dollars,  a 
dress  for  12  dollars,  a  pair  of  shoes  for  2  dollars,  and 
a  parasol  for  3  dollars ;  she  gave   the  merchant  3 
ten   dollar   bills ;    how   many   dollars   must  be   re- 
turned ? 

36.  A  tailor  bought  a  piece  of  cloth  containing  31 
yards,  from  which  he  sold  13  yards  to  one  man,  and 
11  yards  to  another ;  how  many  yards  were  left  of 
the  piece  ? 

37.  A  farmer  had  45  sheep  in  one  lot,  37  in  an- 
other, and   30   in  another  ;   from   the  first  he  sold 
20,  from  the  second  15,  and  from  the  third  12  ;  how 
many  had  he  at  first,  and  how  many  had  he  left? 

38.  A  person,  sitting  down  to  play,  counted  his 
money,  and  found  that  lie  had  1  twenty  dollar  bill,  5 
ten  dollar  bills,  and  3  five  dollar  bills  ;  when  he  got 
up  from  play,  he  had  7  ten  dollar  bills  and  6  five  dol- 
lar bills  ;  did  he  gain  or  lose,  and  how  much  ? 


24  INTELLECTUAL   ARITHMETIC. 

CHAPTER  IIL 
MULTIPLICATION. 

2  times  1  are  how  many  ? ;  2  times  7  are  how  many  ? 
2  times  2  are  how  many  ?|  2  times  8  are  how  many? 
2  times  3  are  how  many  ?  j  2  times  9  are  how  many  ? 


2  -times  4  are  how  many  ? 
2  times  5  are  how  many  ? 

2  times  6  are  how  many? 

3  times  1  are  how  many? 
3  times  2  are  how  many? 
3  times  3  are  how  many  ? 
3  times  4  are  how  many? 
3  times  5  are  how  many? 
3  times  6  are  how  many? 


2  times  10  are  how  many  ? 
2  times  11  are  how  many  ? 

2  times  12  are  how  many  ? 

3  times    7  are  how  many  ? 
3  times    8  are  how  many  ? 
3  times    9  are  how  many  ? 
3  times  10  are  how  many  ? 
3  times  11  are  how  many  ? 
3  times  12  are  how  many  ? 


4  times  1  are  how  many  ?,  4  times  7  are  how  many  ? 
4  times  2  are  how  many  ?!  4  times  8  are  how  many? 
4  times  3  are  how  many  ?  4  times  9  are  how  many  ? 
4  times  4  are  how  many  ?;  4  times  10  are  how  many  ? 
4  times  5  are  how  many?  4  times  11  are  how  many  ? 
4  times  6  are  how  many  ?  4  times  12  are  how  many? 

1.  How  many  are  2  times  6  ?     2  times  8  ?     2 
times  7  ?     2   times  11  ?     2  times  9  ?     2  times  12  ? 

2.  How  many  are  3  times  5  ?     3  times  10  ?     3 
times  9  ?     3  times  7  ?     3  times  6  ?     3  times  12  ? 

3.  How  many  are  4  times  4  ?     4  times  7  ?     4 
times  9  ?     4  times  6  ?     4  times  10  ?     4  times  8  ? 

4.  At  9  dollars  a  ton,  what  will  3  tons  of  hay  cost  ? 

ANALYSIS.  Since  one  ton  costs  9  dollars,  3  tons,  which 
are  3  times  \  ton,  will  cost  3  times  9  dollars  ;  3  times  9 
dollars  are  27  dollars.  Therefore,  at  9  dollars  a  ton, 
3  tons  of  hay  icill  cost  27  dollars. 


13.]  INTELLECTUAL   ARITHMETIC.  25 

5.  At  8  cents  a  quart,  what  will  4  quarts  of  blue- 
berries cost  ? 

6.  If  you  answer  11  questions  at  each  recitation, 
how  many  questions  would  you  answer  at  3  recita- 
tions ?  at  4  ? 

7.  What  will  4  pairs  of  shoes  cost  at  12  shillings 
a  pair  ? 

8.  If  a  ream  of  paper  cost  3  dollars,  what  will  2 
reams  cost  ?  3  reams  ?  4  reams  ? 

9.  Eight  New  York  shillings  make  a  dollar ;  how 
many  shillings  in  3  dollars  ?    in   4   dollars  ?    in   5 
dollars  ? 

10.  At  12  cents  a  yard,  what  will  3  yards  of  calico 
cost  ?  4  yards  ? 


13. 

5  times  1  are  how  many  ?|  5  times  7  are  how  many  ? 
5  times  2  are  how  many  ?  5  times  8  are  how  many  ? 
5  times  3  are  how  many  ?  5  times  9  are  how  many  ? 
5  times  4  are  how  many  ?j5  times  10  are  how  many? 
5  times  5  are  how  many  ?  j  5  times  11  are  how  many? 

5  times  6  are  how  many  ?|5  times  12  are  how  many  ? 

6  times  1  are  how  many  ?|  6  times    7  are  how  many? 
6  times  2  are  how  many  ?  6  times    8  are  how  many  ? 
6  times  3  are  how  many  ?  6  times    9  are  how  many  ? 
6  times  4  are  how  many  ?  6  times  10  are  how  many? 
6  times  5  are  how  many  ?  6  times  11  are  how  many  ? 
6  times  6  are  how  many  ?  6  times  12  are  how  many  ? 

7  times    7  are  how  many  ? 


7  times  1  are  how  many? 
7  times  2  are  how  many  ? 
7  times  3  are  how  many  ? 
7  times  4  are  how  many  ? 
7  times  5  are  how  many  ? 


7  times  8  are  how  many  ? 
7  times  9  are  how  many  ? 
7  times  10  are  how  many? 
7  times  11  are  how  many  ? 


./     I  t/ 

7  times  6  are  how  many  ?!7  times  12  are  how  many? 

3 


26  INTELLECTUAL    ARITHMETIC.  [14. 

1.  How  many  are  5  times  6  ?    5  times  8  ?  5  times 

4  ?  5  times  3  ?  5  times  7  ?  5  times  12  ?  5  times  9  ? 

5  times  11? 

2.  How  many  are  6  times  3  ?  6  times  10  ?  6  times 

6  ?  6  times  9  ?  6  times  7  ?  6  times  11  ?  6  times  8  ? 

6  times  12  ? 

3.  How  many  are  7  times  2  ?  7  times  7  ?  7  times 
4  ?  7  times  9  ?  7  times  12  ?  7  times  10  ?  7  times  8  ? 

7  times  11  ?  7  times  6  ? 

4.  If  you  recite  8  perfect  lessons  in  1  week,  how 
many  would  you  recite  in  5  weeks  ?  in  6  weeks  ?  in 
7  weeks  ? 

5.  What  will  G  pounds  of  sugar  cost  at  10  cents  a 
pound  ?  at  9  cents  ? 

6.  If  you  write  5  lines  a  day,  how  many  lines  will 
you  write  in  4  days  ?  in  7  days  ? 

7.  What  cost  5  yards  of  ribbon,  at  8  cents  a  yard  ? 
at  9  cents  ? 

8.  What  cost  7  barrels  of  apples  at  2  dollars  a 
barrel  ? 

9.  At  12  dollars  a  ton,  what  will  6  tons  of  hay 
cost  ?  7  tons  ?  5  tons  ? 

10.  If  a  boat  sail  9  miles  an  hour,  how  far  will 
she  sail  in  4  hours  ?  in  6  hours  ?  in  7  hours  ? 

11.  What  cost  7  barrels  of  flour,  at  11  dollars  a 
barrel  ? 

12.  There  are  7  days  in  1  week  ;  how  many  days 
in  5  weeks  ?  in  6  weeks  ?  in  9  weeks  ? 

14.  


8  times  1  are  how  many  ?|8  times  7  are  how  many? 
8  rimes  2  are  how  many  ?' 8  times  8  are  how  many? 
8  times  3  are  how  many  ?:8  times  9  are  how  many? 
8  times  4  arc  how  many  ? !  8  times  10  are  how  many  ? 
8  times  5  are  how  many  ?  8  times  11  are  how  many  ? 
f  times  6  are  how  many  ?  1 8  times  12  are  how  many  ? 


14.]  INTELLECTUAL   ARITHMETIC.  27 


9  times  1  arc  how  many  ? 
9  times  2  are  how  many  ? 
9  times  3  are  how  many  ? 
9  times  4  are  how  many  ? 
9  times  5  are  how  many  ? 
9  times  6  are  how  many  ? 


9  times  7  are  how  many  ? 
9  times  8  are  how  many  ? 
9  times  9  are  how  many  ? 
9  times  10  are  how  many  ? 
9  times  11  are  how  many  ? 
9  times  12  are  how  many  ? 


10  times  1  are  how  many  ?  1 10  times    7  are  how  many  ? 
10  times  2  are  how  many  ?  j 10  times    8  are  how  many  ? 


10  times  3  are  how  many  ? 
10  times  4  are  how  many  ? 
10  times  5  are  how  many  ? 
10  times  6  are  how  many  ? 


10  times  9  are  how  many  ? 
10  times  10  are  how  many  ? 
10  times  11  are  how  many  ? 
10  times  12  are  how  many  ? 


1.  How  many  are  8  times  6  ?  8  times  4  ?  8  times 
9  ?  8  times  5  ?  8  times  10  ?     8  times  7  ?  8  times  11  ? 

8  times  8  ?  8  times  12  ? 

2.  How  many  are  9  times  3  ?  9  times  7  ?  9  times 
4  ?  9  times  6  ?  9  times  8  ?  9  times  12  ?  9  times  9  ? 

9  times  5  ?  9  times  11  ?  9  times  10  ? 

3.  How  many  are  10  times  10  ?  10  times  8  ?  10 
times  4  ?  10  times  7  ?  10  times  11  ? 

4.  What  will  8  barrels  of  flour  cost,  at  9  dollars  a 
barrel  ? 

5.  What  will  9  chairs  cost,  at  10  shillings  apiece  ? 

6.  If  5  boys  can  sit  on  one  bench,  how  many  can 
sit  on  7  benches  ?  on  8  benches  ? 

7.  If  Harvey  can  earn  10  dollars,  in  one  month, 
how  many  dollars  can  he  earn  in   8  months  ?   in  9 
months  ?  in  7  months  ? 

8.  If  8  men  can  do  a  piece  of  work  in  7  days,  how 
many  days  will  it  take  one  man  to  do  it  ? 

9.  If  two  barrels  of  flour  last  8  persons  3  months, 
how  long  will  they  last  one  person  ? 

10.  How  many  dollars  will  buy  10  tons  of  hay,  at 
12  dollars  a  ton? 


28  INTELLECTUAL   ARITHMETIC. 

11.  A  farmer  divided  his  farm  into  9  fields,  con- 
taining   11    acres   each ;    how   many   acres   in    his 
farm  ? 

12.  If  a  man  travel  6  miles  an  hour,  how  far  will 
he  travel  in  7  hours  ?  in  8  hours  ?  in  9  hours  ?  in  6 
hours  ? 

13.  When  eggs  are  11  cents  a  dozen,  what  will  be 
lie  cost  of  7  dozen  ?  of  9  dozen  ?  of  10  dozen  ? 


13. 

11  times  1  are  how  many  ? 
11  times  2  are  how  many  ? 
11  times  3  are  how  many  ? 
11  times  4  are  how  many  ? 
11  times  5  are  how  many  ? 


11  times  7  are  how  many  ? 
11  times  8  are  how  many  ? 
11  times  9  are  how  many  ? 
11  times  10  are  how  many  ? 
11  times  11  are  how  many  ? 


v 


11  times  6  are  how  many  ?  11  times  12  are  how  many  ? 

12  times  1  are  how  many  ?  ( 12  times    7  are  how  many  ? 
12  times  2  are  how  many  ?  j  12  times    8  are  how  many  ? 
12  times  3  are  how  many  ?  12  times    9  are  how  many  ? 
12  times  4  are  how  many  ?  12  times  10  are  how  many  ? 
12  times  5  are  how  many  ?  12  times  11  are  how  many  ? 
12  times  6  are  how  many  ?  12  times  12  are  how  many  ? 

1.  How  many  are  11  times  6  ?  11  times  10  ?  11 
times  7  ?  11  times  12  ?  11  times  8  ?     11  times  11  ? 

11  times  5  ? 

2.  How  many  are  12  times  10  ?  12  times  9  ?  12 
times  7  ?  12  times  8  ?  12  times  6  ?     12  times  11  ? 

12  times  5  ?  12  times  12  ? 

3.  What  will  be  the  cost  of  11  bunches  of  grapes, 
at  10  cents  a  bunch  ? 

4.  What  will  be  the  cost  of  12  barrels  of  pork,  at 
11  dollars  a  barrel  ? 

5.  What  will  11  yards  of  cloth  cost,  at  6  dollars  a 
yard  ? 


15.]  INTELLECTUAL   ARITHMETIC.  29 

6.  In  an  orchard  are  12  rows  of  trees,  and  11 
trees  in  each  row  ;  how  many  trees  in  the  orchard  ? 

7.  What  will  11  turkeys  cost  at  6  dimes  apiece  ? 
at  7  dimes  ? 

8.  At  12  dollars  a  hundred,  what  will  7  hundred 
oak  posts  cost  ?     9  hundred  ?     11  hundred  ? 

9.  At  9  dollars  a  week,  what  will  5  weeks'  board 
cost  ?     8  weeks'  ?     11  weeks'  ?     12  weeks'  ? 

10.  If  the  fare  for  one  person  from  Albany  to  Bos- 
ton is  5  dollars,  what  will  be  the  fare  for  6  persons  ? 
for  9  persons  ?  for  12  persons  ? 

11.  At  12  dollars  a  month,  how  many  dollars  can 
a  man   earn  in   4   months  ?    in   6    months  ?    in   9 
mouths  ?  in  12  months  ? 

12.  If  it  take  9  yards  of  calico  for  one  dress,  how 
many  yards  will  be  required  to  make  4  dresses  ?   7 
dresses  ? 

13.  If  a  farmer  put  his   oats    into  7   bins,  each 
containing  12  bushels,  how  many  bushels  has  he  ? 

14.  If  I  put  8  dollars  in  the  savings  bank  every 
month,  how  many  dollars  will  I  deposit  in  7  months  ? 
in  8  months  ?  in  12  months  ? 

15.  What  will  11  dozen  of  eggs  cost,  at  9  cents 
a  dozen  ?  at  10  cents  ?  at  11  cents  ? 

16.  If  a  quantity  of  provision  will  last  9  men  12 
days,  how  long  will  the  same  provision  last  one  man  ? 

17.  When  flour  is  7  dollars  a  barrel,  what  must 
be  paid  for  7  barrels  ?  for  8  barrels  ?   for  9  barrels  ? 
for  11  barrels  ? 

18.  If  12  bushels  of  apples  be  picked  from  each 
of  11  trees,  how  many  bushels  will  be  picked  from 
all? 

1 G.  Multiplication  is  the  process  of  finding  a  number  which  shall 
contain  one  of  two  given  nu:nbers  as  many  times  as  there  are  units  in 
the  other  j  the  result  is  called  the  Product. 


30  INTELLECTUAL   ARITHMETIC.  [16. 

The  sign  of  multiplication  is  written  thus,  X,  and,  placed 
between  two  numbers  or  quantities,  shows  that  they  are  to 
be  multiplied  together.  5  X  4  =  20,  shows  that  5  multi- 
plied by  4  is  equal  to  20.  The  sign  is  commonly  called 
times.  5  X  4  is  read  5  times  4. 


1.  5x3  are  how  many  ? 

2.  7x4  are  how  many  ? 

3.  10x7  are  how  many? 

4.  3x8  are  how  many  V 

5.  7x9  are  how  many  ? 

6.  12x6  are  how  many  ? 

7.  9x8  are  how  many  ? 


8.  8x11  are  how  many  ? 

9.  6x9  are  how  many  ? 

10.  5x7  are  how  many  ? 

11.  11  xlO  are  how  many  ? 

12.  8x4  are  how  many? 

13.  11 X 11  are  how  many  ? 

14.  12  x  12  are  how  many  ? 


15.  What  is  the  product  of  7  X  6  ?  of  9  X  5  ? 
of  7  X  7  ?  of  11  X  6  ? 

16.  What  is  the  product  of  4x3x2?  of  5x 
2  X  3?  of  3  X  3  X9? 

17.  What  will  be  the  cost  of  3  cows,  at  23  dollars 
apiece  ? 

ANALYSIS.  Since  1  cow  cost  23  dollars,  3  cows,  which 
are  3  times  1  cow,  will  cost  3  times  23  dollars.  23  is  equal 
to  2  tens  and  3  units  ;  3  times  3  units  are  9  units,  and  3 
times  2  tens  are  6  tens,  or  GO ;  60  and  9  are  69.  Therefore, 
if  \  cow  cost  23  dollars,  3  cows  will  cost  69  dollars. 

18.  At  31  cents  a  bushel,  what  will  be  the  cost  of 
6  bushels  of  oats  ? 

19.  What  will  be  the  cost  of  7  bushels  of  apples, 
at  25  cents  a  bushel  ? 

20.  If  a  man  travel  26  miles  in  one  day,  how  far 
can  he  travel  in  10  days  ? 

21.  Mary  bought  6  yards  of  muslin  at  18  cents  a 
yard  ;  what  was  the  cost  of  the  whole  ? 

22.  Ephraim  is  17  years  old,  and  his  father  is  4 
times  as  old  ;  how  old  is  his  father  ? 


16.]  INTELLECTUAL   ARITHMETIC.  31 

23.  At  50  dollars  a  share,  what  will  7  shares  of 
bank  stock  cost  ? 

24.  What  will  9  pounds  of  tea  cost,  at  56  cents  a 
pound  ? 

25.  At  44  cents  a  day,  what  will  10  days'  labor 
amount  to  ? 

26.  At  3  dollars  a  yard,  what  will  be  the  cost  of  a 
piece  of  cloth  containing  36  yards  ? 

27.  What  will  be  the  cost  of  12  pounds  of  coffee, 
at  15  cents  a  pound  ? 

28.  If  the  cars  run  24  miles  an  hour,  how  far  will 
they  run  in  7  hours  ? 

29.  In  an  orchard  are  16  peach  trees,  and  6  times 
as  many  apple  trees ;  how  many  apple  trees  in  the  , 
orchard  ? 

30.  What  will  be  the  cost  of  45  lemons,  at  5  cents 
apiece  ? 

31.  If  11  men  can  do  a  piece  of  work  in  13  days, 
in  what  time  will  one  man  do  the  same  work  ? 

32.  If  a  man  labor  12  months  for  17  dollars  a 
month,  how  much  will  his  wages  amount  to  ? 

33.  At  3  dollars  a  barrel,  what  will  be  the  cost  of 
28  barrels  of  potatoes  ? 

34.  If  in  an  orchard  are  12  rows  of  trees,  and 
32  trees  in  each  row,  how  many  trees  in  the  or- 
chard ? 

35.  If  a  man  can  dig  28  bushels  of  potatoes  iii  ono 
clay,  how  many  bushels  can  he  dig  in  3  days  ?  in  4 
days  ?  in  5  days  ? 

36.  At  80  dollars  apiece,  what  will  be  the  cost  of 
3  horses  ?  of  4  horses  ?  of  6  horses  ? 

37.  At  43  dollars  an  acre,  what  will  10  acres  of 
land  cost  ?     12  acres  ? 

38.  If  8  horses  eat  3  bushels  of  oats  in  one  day, 
how  many  bushels  will  they  eat  in  7   days  ?   in  9 
days? 


82  INTELLECTUAL   ARITHMETIC.  [17. 

17.  1.  What  will  be  the  cost  of  6  tons  of  coal, 
at  5  dollars  a  ton,  and  of  4  cords  of  wood  at  3  dol- 
lars a  cord  ? 

ANALYSIS.  They  will  cost  the  sum  of  the  products  of 
0  X  o  dollars,  and  of  4  X  3  dollars  ;  6  times  5  dollars  are 
30  dollars,  and  4  times  3  dollars  are  1 2  dollars ;  30  dollars 
and  12  dollars  are  42  dollars.  Therefore,  fyc. 

2.  A  farmer  sold  12  sheep  at  4  dollars  a  head, 
and  9  lambs  at  2  dollars  each ;  how  many  dollars 
did  he  receive  for  all  ? 

3.  What  will  be  the  cost  of  5  pounds  of  coffee  at 
15  cents  a  pound,  and  14  pounds  of  rice  at  6  cents  a 
pound  ? 

4.  If  two  persons  start  from  the  same  point,  and 
travel  in  opposite  directions,  one  at  the  rate  of  6 
miles  an  hour,  and  the  other  4  miles  an  hour,  how 
far  apart  will  they  be  in  7  hours  ?  in  9  hours  ?  in  12 
hours  ? 

5.  If  they  travel  in  the  same  direction,  how  far 
apart  will  they  be  in  5  hours  ?  in  7  hours  ?  in  24 
hours  ? 

6.  If  I  hire  a  man  and  his  son  to  labor,  the  father 
at  14  shillings  a  day,  and  the  son  at  8  shillings,  how 
much  will  be  due  them  both  in  6  days  ?  in  9  days  ? 

7.  Asa  has   16   marbles,  and   Omar   3  times  as 
many  ;  how  many  have  both  ? 

8.  A  drover  bought  28  sheep  at  3  dollars  a  head, 
and  5  cows  at  26  dollars  apiece ;  what  was  the  cost 
of  the  whole  ? 

9.  Justin  bought  9  oranges  at  4  cents  apiece,  7 
lemons  at  3  cents  apiece,  and  10  load  pencils  at  2 
cents  apiece ;  how  much  was  the  cost  of  the  whole  ? 

10.  Charles  is  twice  as  old  as  Byron,  and  Byron  is 
14  years  old ;  what  is  the  sum  of  their  ages  ? 

11.  In  a  school-room  16  pupils  can  sit  on  each 


18.]  INTELLECTUAL   ARITHMETIC.  33 

of  5  seats,  8  on  each  of  3  seats,  and  20  on  the  re- 
mainder of  the  seats ;  how  many  pupils  can  be  seat- 
ed in  the  room  ? 

12.  A  farmer  has  30  sheep  in  each  of  3  pastures, 
35  in  each  of  2  pastures,  and  40  in  another   pas- 
ture ;  how  many  sheep  has  he  in  all  ? 

13.  If  one  boy  earns  12  cents  a  day,  another  15 
cents  a  day,  and  another  20  cents  a  day,  how  much 
can  the  3  boys  earn  in  5  days  ? 

14.  A  man  bought  9  yards  of  cloth  for  a  suit  of 
clothes,  at  5  dollars  a  yard ;  he  paid  7  dollars  for 
making  the  coat,  2  dollars  for  making  the  pantaloons, 
and  1  dollar  for  making  the  vest ;  what  did  his  suit 
cost  him  ? 


18.  1.  A  farmer  bought  a  horse  for  85  dollars, 
for  which  he  gave  7  tons  of  hay  at  9  dollars  a  ton, 
and  the  remainder  in  money  ;  how  much  money  did 
he  pay  ? 

ANALYSIS.  He  paid  in  money,  the  difference  between 
85  dollars  and  the  product  of  7  times  9  dollars  ;  1  times  9 
dollars  are  63  dollars,  and  85  dollars  less  63  dollars  are  22 
dollars.  Tfierefore,  §c. 

2.  John  worked  5  days  for  15  cents  a  day,  and 
Norman  worked  4  days  for  20  cents  a  day ;  how 
much  more  did  Norman  earn  than  John  ? 

3.  A  drover  bought  35  sheep  at  2  dollars  a  head, 
and  sold  them  for  90  dollars ;  how  much  did  he  gain  ? 

4.  A  mechanic   earned   32   dollars   a  month  for 
five  months,  and  his  apprentice  12  dollars  a  month 
for  the  same  time  ;  how  much  more  did  the  one  earn 
than  the  other  ? 

5.  If  a  man  earn  90  cents  a  day,  and  pay  40  cents 
a  day  for  his  board,  how  much  will  he  save  in  6  days  ? 


84  INTELLECTUAL   ARITHMETIC.  [18. 

6.  A  farmer  sold  a  grocer  7  pounds  of  butter  at 
20  cents  a  pound,  and  received  in  payment  12  pounds 
of  fish  at  6  cents  a  pound ;  how  much  was  still  due 
the  farmer  ? 

7<  How  much  difference  does  Mr.  Jones  receive, 
by  exchanging  5  cows  at  18  dollars  a  head,  for  7 
head  of  young  cattle,  at  9  dollars  each  ? 

8.  A  merchant  poured  into  a  cask  14  quarts  of 
camphene  3  different  times,  and  from  the  same  cask 
filled  2  cans,  holding  8  quarts  each,  and  8  jugs,  hold- 
ing 6  quarts  each ;   how  many  quarts  remained  in 
the  cask  ? 

9.  Nellie  picked   6  quarts    of  blackberries,  and 
Laura  picked  4  times  as  many,  wanting  5  quarts  ; 
how  many  quarts  did  Laura  pick  ? 

10.  What  is  the  difference  in  the  cost  of  30  yards 
of  cloth  at  4  dimes  a  yard,  and  25  yards  at  3  dimes 
a  yard  ? 

11.  A  lady  bought  6  yards  of  satin,  at  2  dollars  a 
yard,  2  shawls  at  9  dollars  each,  and  some  lace  for  3 
dollars ;  she  paid  4  ten  dollar  bills ;  how  much  ought 
she  to  receive  back  ? 

12.  A  drover  bought  50  sheep  for  125  dollars  ;  he 
sold  30  at  4  dollars  a  head,  and  the  remainder  at 
3  dollars  a  head ;  how  many  dollars  did  he  gain  by 
the  bargain  ? 

13.  Three  boys  talking  of  their  money,  one  said 
he  had  35  cents,  another  said  he  had  twice  as  many, 
and  the  third  said  he  had  as  many  as  both  the  others, 
wanting  10  cents  ;  how  many  cents  had  the  last  ? 

14.  Two  men  bought  a  horse  for  75  dollars  ;  they 
paid  2  dollars  a  week  for  keeping  him,  and  at  the 
end  of  12  weeks  sold  him  for  90  dollars ;  how  much 
did  they  lose  by  their  bargain  ? 

15.  A  man,  owing  100  dollars,  gave  a  sleigh  worth 
40  dollars,  12  cords  of  wood,  at  3  dollars  a  cord, 


18.]  INTELLECTUAL   ARITHMETIC.  36 

and  the  remainder  in  money ;  how  much  money  did 
he  pay  ? 

16.  I  bought  a  book-case  for  28  dollars,  a  table 
for  14  dollars,  and  6  chairs  at  2  dollars  each ;  I  paid 
for  the  table  ;  how  much  did  I  still  owe  ? 

17.  If  a  blacksmith  earn  14  shillings  a  day,  and  a 
joiner  11  shillings  a  day,  what  will  the  difference  in 
their  earnings  amount  to  in  12  days  ? 

18.  Perry  paid  3  cents  for  a  lemon,  Elisha  twice 
as  much  for  a  pineapple,  and  for  a  melon  Albert  paid 
5  times  as  much,  lacking  15  cents,  as  was  paid  for 
both  the  lemon  and  the  pineapple ;  what  would  be 
the  cost  of  3  melons  at  the  same  rate  ? 

19.  At  a  public  meeting  are  35   gentlemen,  and 
3  times  as  many  ladies  lacking  30  ;  how  many  ladies 
are  there,  and  how  many  ladies  and  gentlemen  ? 

20.  Peter  has  4  times  5  peaches,  and  Marcus  has 
3  times  6 ;  how  many  will  they  both  have  left  after 
Peter  gives  away  7,  and  Marcus  5  ? 

21.  How  many  are  4  times  20,  plus  3  times  10  2 

22.  How  many  are  7  times  15,  plus  9  times  12  ? 

23.  How  many  are  12  times  11,  minus  10  times  7  ? 

24.  How  many  are  10  times  11,  less  15,  plus  6 
times  5  ? 

25.  How  much  less  is  7  times  14,  than  3  times  40  ? 

26.  How  much  less  is  10  times  10,  than  6  times 
20  plus  25  ? 

27.  How  much  more  is  8  times  16,  than  7  times 
13  minus  11  ? 

28.  How  many  are  9  times  12,  plus  22  +  10  —  30  ? 

29.  How  many  are  15  X  12,  +  20  X  5  ? 

30.  How  many  are  40  X  4,  +  27  X  3  ? 

31.  How  many  are  16  X  9,  —  13  X  6  ? 

32.  How  many  are  10  +  12,  X  6,  —  40  ? 

33.  How  many  are  14  X  8,  +  18,  +  12,  —  7  2 


36  INTELLECTUAL   ARITHMETIC.  [19. 

CHAPTER  IV. 
DIVISION. 

19.  1.  WHEN  wheat  is  2  dollars  a  bushel,  how 
many  bushels  can  be  bought  for  12  dollars  ? 

ANALYSIS.  Since  2  dollars  will  bin/  1  bushel,  12  dol- 
lars will  buy  as  many  bushels  as  2  dollars,  the  price  of  \ 
bushel,  is  contained  times  in  12  dollars  /  2  dollars  is 
contained  in  12  dollars  0  times.  Therefore,  at  2  dollars 
a  bushel,  6  bushels  of  wheat  can  be  bought  for  12  dollars. 

2.  How  many  peaches  at  2  cents  apiece,  can  bo 
bought  for  18  cents  ? 

3.  If  you  can  buy  one  lead  pencil  for  3  cents,  how 
many  can  you  buy  for  24  cents  ? 

4.  For  16  dollars,  how  many  cords  of  wood  can 
be  bought  at  4  dollars  a  cord  ? 

5.  At  3  cents  apiece,  how  many  oranges  can  be 
bought  for  21  cents  ? 

6.  In  how  many  days  can  a  man  earn  20  dollars, 
if  he  earn  2  dollars  a  day  ? 

7.  Edward  has  15  peaches,  which  he  wishes  to  di- 
vide equally  among  his  3  brothers  ;  how  many  must 
he  give  to  each  ? 

8.  How  many  times  2  in  8  ?  in  6  ?  in  10  ?  in  14  ? 
in  16  ?  in  20  ?  in  24  ? 

9.  How  many  times  3  in  6  ?    in  12  ?   in  18  ?   in 
21  ?  in  9  ?  in  27  ?  in  33  ?  in  24  ?  in  36  ? 

10.  How  many  times  4  in  12  ?  in  8  ?  in  16  ?  in 
20  ?  in  36  ?  in  24  ?  in  40  ?  in  32  ?  in  48  ? 

11.  How  many  tons  of  coal,  at  4  dollars  a  ton, 
can  be  bought  for  48  dollars  ? 

12.  If  one  penholder  can  be  bought  for  4  cents, 
how  many  can  be  bought  for  20  cents  ?  for  32  cents  ? 
for  40  cents  ? 


INTELLECTUAL   ARITHMETIC.  37 

13.  Paid  36  dollars  for  3  gold  chains ;  what  was 
the  cost  of  each  ? 

14.  How  many  barrels  of  apples,  at  3  dollars  a 
barrel,  can  be  bought  for  36  dollars  ? 

15.  If  you  give  44  cents  to  4  beggars,  how  many 
do  you  give  to  each  ? 

16.  If  a  man  walk  3  miles  an  hour,  how  many 
hours  will  it  take  him  to  walk  30  miles  ? 

17.  Bought  4  barrels  of  flour  for  28  dollars  ;  what 
was  the  cost  of  one  barrel  ? 

18.  If  I  pay  27  cents  for  3  pounds  of  sugar,  how 
much  do  I  pay  a  pound  ? 

19.  15  are  how  many  times  3  ?  5  ? 

20.  86  are  how  many  times  3  ?  6  ?  4  ? 

21.  42  are  how  many  times  6  ?  7  ?  3  ? 

22.  24  are  how  many  times  2  ?  6  ?  4  ?  8  ? 

23.  16  are  how  many  times  4  ?  2  ?  8  ? 

24.  40  are  how  many  times  8  ?  5  ?  4  ? 

25.  72  are  how  many  times  8  ?  6  ?  12  ? 

26.  56  are  how  many  times  7  ?  8  ?  4  ? 

27.  48  are  how  many  times  4  ?  6  ?  8  ?  12  ? 

28.  32  are  how  many  times  8  ?  2  ?  4  ? 

29.  30  are  how  many  times  5  ?  6  ?  3  ? 


SO.     1.   How  many  spools  of  thread,  at  5  cents  a 
spool,  can  be  bought  for  40  cents  ?  for  50  cents  ? 

2.  When   lard  is   7   cents   a  pound,  how  many 
pounds  can  be  bought  for  56  cents  ?  for  63  cents  ? 

3.  If   a   farmer   divide   84    bushels   of  potatoes 
equally  among  7  laborers,  how  many  bushels  will 
each  receive  ? 

4.  If  an  orchard  contain  64  trees,  and  8  trees  in  a 
row,  how  many  rows  are  there  ? 

5.  If  a  man  travel  72  miles  ia  6  hours,  how  far 
does  he  travel  in  one  hour  ? 


88  INTELLECTUAL   ARITHMETIC.  [2O. 

6.  Levi  paid  7  cents  for  his  ball ;  how  many  balls 
at  the  same  price  could  he  buy  for  28  cents  ?  for 
56  cents  ?  for  63  cents  ?  for  84  cents  ? 

7.  How  many  bins  will  be  required  to  hold  72 
bushels  of-  wheat,  if  each  bin  contain  8  bushels  ? 

8.  At  5  dollars  a  week,  how  long  will  it  take  a 
man  to  earn  45  dollars  ?  50  dollars  V 

9.  At  8   cents   a   pound,    how  many  pounds   of 
sugar  can  be  bought  for  96  cents  ? 

10.  If  a  man  spend  6  cents  a  day  for  cigars,  how 
many  days  will  60  cents  last  him  ? 

11.  A  man  bought  some  sheep  for  48  dollars,  at 
4  dollars  apiece  ;  how  many  sheep  did  he  buy  ? 

12.  If  one  man  can  do  a  job  of  work  in  60  days, 
in  what  time  can  5  men  do  the  same  work  ? 

13.  45  are  how  many  times  5  ?  9  ?  3  ? 

14.  36  are  how  many  times  4  ?  6  ?  9  ?  12  ? 

15.  80  are  how  many  times  10  ?  8  ?  4  ?  5  ? 

16.  9l>  are  how  many  times  8  ?  6  ?  12  ?  4  ? 

17.  44  are  how  many  times  11  ?  4  ?  2  ? 

18.  24  are  how  many  times  2  ?  8  ?  4  ?  6  ?  12  ? 

19.  60  are  how  many  times  6  ?  5  ?  10  ?  12  ? 

20.  63  are  how  many  times  9  ?  3  ?  7  ? 

21.  84  are  how  many  times  7  ?  12  ?  4  ?  6  ? 

22.  90  are  how  many  times  9  ?  6  ?  10  ? 

23.  108  are  how  many  times  12  ?  9  ?  6  ? 

24.  100  are  how  many  times  10  ?  20  ?  5  ? 

25.  99  are  how  many  times  9  ?  11  ?  3  ? 

26.  81  are  how  many  times  9  ? 

27.  66  are  how  many  times  11  ?  6  ?  3  ? 

28.  75  are  how  many  times  15  ?  5  ?  25  ? 

29.  88  are  how  many  times  4  ?  11  ?  8  ? 

30.  120  are  how  many  times  12  ?  10  ?  8  ? 

31.  140  are  how  many  times  7  ?  10  ?  20  ? 
82.   200  axe  how  many  times  20  ?  40  ?  50  ? 


31.]  INTELLECTUAL    VRITHMETIC.  39 

31.  1.  If  6  men  receive  72  dollars  for  building 
a  barn,  how  many  dollars  will  each  man  receive  ? 

NOTE.  If  the  pupil  is  sufficiently  acquainted  with  Fractions, 
the  following  Analysis  is  often  preferred.* 

ANALYSIS.  If  6  men  receive  72  dollars,  1  man,  which 
is  ^  of  Q  men,  will  receive  \  of  72  dollars  •  ^  of  72  dol- 
lars is  12  dollars.  Therefore  if  6  men  receive  72  dol- 
lars for  building  a  barn,  each  man  will  receive  12  dollars. 

2.  If  81  cents  be  paid  for  9  dozen  of  eggs,  what 
will  be  the  cost  of  1  dozen  ? 

3.  A  mechanic  sold  a  wagon  for  77  dollars,  and 
took  his  pay  in  hay,  at  11  dollars  a  ton ;  how  many 
tons  did  he  receive  ? 

4.  How  long  will  it  take  12  men  to  perform  a 
piece  of  work  that  1  man  can  do  in  48  days  ? 

5.  Paid  108  dollars  for  9  thousand  feet  of  lum- 
ber ;  what  was  the  COSY  of  a  thousand  feet  ? 

6.  How  many  barrels  of  flour  can  be  bought  for 
56  dollars,  at  7  dollars  a  barrel  ?  at  8  dollars  ? 

7.  How  many  cows,  at  12  dollars  a  head,  can  be 
bought  for  60  dollars?  for  9n  dollars?  for  120  dollars? 

8.  When  steak  is  10  cents  a  pound,  how  many 
pounds  can  be  bought  for  50  cents  ?  for  80  cents  ? 
for  100  cents  ? 

9.  At  11  cents  a  pound,  ho\v  many  pounds  of 
sugar  can  be  bought  for  88  cents  ?  for  99  cents  ? 

*  When  it  is  necessary  to  express  a  quantity  less  than  a  unit,  we  may 
regard  the  unit  as  divided  iiito  some  number  of  equal  parts,  and  use 
cue  of  these  parts  as  a  new  unit  of  less  value  thau  the  unit  divided. 
Thus,  if  a  yard  be  divided  into  two  equal  parts,  each  of  the  parts  is 
called  one  half;  when  into  three  equal  parts,  each  of  tue  parts  is  called 
one  third  •  wuen  into  four  equal  parts,  each  of  the  j>arts  is  called  one 
fourth  ;  when  into  Jive  equal  parts,  each  of  the  parts  is  called  one-fifth  ; 
two  of  the  parts,  two  fifths,  &c. ;  when  into  six  equal  parts,  each  of  the 
parts  is  called  one  sixth  ;  two  of  the  parts,  two  sixths,  three  of  the  parts, 
three  sixths }  &c. 


40  INTELLECTUAL   ARITHMETIC.  [91. 

10.  A  man  planted  an  orchard  of  132  trees,  and 
put  11  trees  in  a  row ;  how  many  rows  in  the  orchard  ? 

11.  A  farmer  sold  a  horse  for  120  dollars;  how 
many  cows  at  12  dollars  each  would  pay  for  the 
horse  ?     How  many  young  cattle  at  8  dollars  each  ? 
How  many  sheep  at  5  dollars  each  ? 

12.  If  25  sheep  cost  75  dollars,  what  will  1  sheep 
cost? 

13.  If  a  boy  read  7  pages  a  day,  how  long  will  it 
take  him  to  read  56  pages?  to  read  84  pages?  98 
pages  ? 

14.  At  15  cents  a  pound,  how  many  pounds  of 
coffee  can  be  bought  for  45  cents  ?  for  60  cents  ?  for 
90  cents  ? 

15.  If  1  man  can  do  a  piece  of  work  in  72  days, 
in  what  time  can  6  men  do  it  ?  8  men  ?  9  men  ?  12 
men? 

16.  If  a  certain  quantity  of  provision  will  last  1 
man  36  days,  how  many  days  will  it  last  4  men  ?  9 
men  ?  12  men  ? 

17.  A  man  earns  66  dollars  in  11  weeks ;  how 
ttmfch  does  he  earn  in  1  week  ?  how  much  in  1  day  ? 

18.  If  a  painter  receive  100  dollars  for  painting  5 
carriages,  how  much  does  he  receive  apiece  ? 

19.  How  many  lots  containing  12  acres  each  can 
be  sold  from  a  farm  of  120  acres  ?  how  many  lots  of 
20  acres  each  ? 

20.  If  a  steamboat  run  11  miles  an  hour,  how 
long  will  she  be  in  running  44  miles  ?  88  miles  ? 
110  miles  ? 

21.  How  many  men,  at  8  dollars  a  month,  can  be 
hired  one  month  for  96  dollars?  how  many  at  12 
dollars  ?  how  many  at  16  dollars  ? 

22.  If  I  travel  120  miles  in  6  days,  how  many 
miles  do  I  travel  in  1  day  ? 


INTELLECTUAL   ARITHMETIC.  41 

1.   If  3  pounds  of  coffee  cost  27  cents,  what 
will  6  pounds  cost  ? 

ANALYSIS.  If  3  pounds  of  coffee  cost  27  cents,  1  pound, 
which  is  1  third  of  3  pounds,  will  cost  1  third  of  27  cents, 
or  9  cents.  If  1  pound  cost  9  cercto,  6  pounds,  which  are 

6  times   1  pound,  will  cost   6  ft'mes   9  cento,  or  54  cents. 
Therefore,  if  3  pounds  of  coffee  cost  27  cento,  6  pounds  will 
cost  54  cents. 

Or  thus  :  C  pounds  will  cost  6  ta'wes  1  third  of  27  ce??to;  1 
<AiVc?  o/  27  cento  is  9  cento,  awe?  6  times  9  cento  are  54  cents. 
Therefore,  fyc. 
Or  6  pounds,  which  are  2  foVwes  3  pounds  will  c^st  2  times  27  cente,  <fcc. 

2.  If  4  yards  of  broadcloth  cost  20  dollars,  what 
will  9  yards  cost  ? 

3.  If  6  barrels  of  flour  cost  54  dollars,  what  will 

7  barrels  cost  ? 

4.  If  9  yards  of  ribbon  cost  72  cents,  what  will 
4  yards  cost  ? 

5.  If  a  man  travel  40  miles  in  8  hours,  how  far 
will  he  travel  in  6  hours  ?  in  9  hours  ? 

6.  If  5  coats  can  bo  cut  from  20  yards  of  cloth, 
how  many  yards  would  be  required  to  cut  7  coats  ? 

'     7.   If  9  weeks'  board  cost  45  dollars,  what  will  4 
weeks'  board  cost  ?  7  weeks'  ?  12  weeks'  ? 

8.  If  a  boy  earn  60  cents  in  5  days,  how  many 
cents  will  he  earn  in  12  days  ?  in  20  days  ? 

9.  What  will  be  the  cost  of  10  cords  of  wood,  if 
6  cords  cost  24  dollars  ? 

10.  What  will  be  the  cost  of  14  dozen  of  eggs,  if 
12  dozen  cost  120  cents  ? 

11.  If  18  apples  are  worth  6  peaches,  how  many 
apples  are  15  peaches  worth  ?  20  peaches  ? 

12.  If  a  stage  coach  run  48  miles  in  8  hours,  in 
how  many  hours  will  it  run  60  miles  ? 

13.  If  15  yards  of  cloth  cost  75  dollars,  what  will 
40  yards  cost  ? 

4* 


42  INTELLECTUAL   ARITHMETIC. 

14.  How   many  melons   can  be   bought  for  100 
/ents,  at  the  rate  of  3  for  60  cents  ? 

15.  What  will  42  pounds  of  beef  cost,  if  7  pounds 
cost  56  cents  ? 

16.  When  apples  are  sold  at  the  rate  of  4  barrels 
for  8  dollars,  how  many  barrels  must  be  given  for  3 
tons  of  coal  at  6  dollars  a  ton  ? 

17.  How  many  dozen  of  eggs,  at  12  cents  a  dozen, 
will  pay  for  15  pounds  of  sugar,  at  8  cents  a  pound  ? 

18.  How  many  gallons  of  molasses,  at  t,G  cents  a 
gallon,  will  pay  for  20  pounds  of  lard,  worth  10  cents 
a  pound  ? 

19.  If  a  farmer  sell  5  firkins  of  butter,  worth  12 
dollars  a  firkin,  for  cloth  worth  4  dollars  a  yard,  how 
many  yards  will  he  receive  ? 

20.  If  5  barrels  of  cider  are  worth  15  dollars,  how 
many  hundred  weight  of  pork,worth  6  dollars  a  hun- 
dred weight,  would  8  barrels  of  cider  buy  ? 

21.  If  6  bushels  of  wheat  are  worth  12  dollars, 
how  many  bushels  of  wheat  must  be  given  for  9  tons 
of  hay,  worth  10  dollars  a  ton  ? 

22.  At  the  rate  of  3  for  4  cents,  how  many  pears 
can  be  bought  for  24  cents  ? 

ANALYSIS.  Since  4  cents  will  buy  3  pears,  24  cents  will 
buy  as  many  times  3  pears  as  4  cents  is  contained  times 
in  124  cents  ;  4  cents  are  contained  in  24  cents  6  times, 
and  6  times  3  are  1 8  pears.  Therefore,  if  3  pears  can  be 
bought  for  4  cents,  IS  pears  may  be  bought  for  24  cents. 

23.  A  man  paid  72  cents  for  some  oranges,  at  the 
rate  of  5  for  12  cents  ;  how  many  oranges  did  he  buy? 

24.  How  many  pounds  of  nails  may  be  bought  for 
60  cents,  at  the  rate  of  4  pounds  for  20  cents  ? 

25.  When  eggs  are  sold  at  the  rate  of  9  for  11 
cents,  how  many  must  be  sold  to  receive  99  cents  ? 

26.  At  the  rate  of  16  miles  in  4  hours,  how  many 
miles  would  a  man  travel  in  12  hours  ? 


INTELLECTUAL   ARITHMETIC.  •         43 

27.  If  8  men  can  do  a  piece  of  work  in  12  days, 
how  many  days  will  it  take  9  men  to  do  the  same  ? 

ANALYSIS.  If  3  men  can  do  the  work  in  12  days, 
9  men  can  do  it  in  ^  of  3  times  12  days  /  3  times  12 
days  are  36  days,  and  ^  of  36  days  are  4  days.  There- 
fore, <&c. 

28.  If  6  men  can  build  a  wall  in  8  days,  how 
many  men  will  be  required  to  build  it  in  3  days  ? 

29.  If  4  men  can  dig  a  ditch  in  10  days,  how 
many  days  will  it  take  1  man  to  dig  it  ?  5  men  ?  8 
men  ? 

30.  How  long  will  it  take  7  men  to  reap  a  field, 
if  it  take  14  men  2  days  to  reap  it  ? 

31.  If  5  men  can  build  a  barn  in  8  days,  how 
many  men  would  be  required  to  build  it  in  1  day  ? 
in  2  days  ?  in  4  days  ? 

32.  A  man  bought  some  oranges  for  44  cents,  at 
the  rate  of  5  for  11  cents,  and  divided  them  equally 
among  his  4  children ;   how  many  did  he  give  to 
each  ? 

33.  If  15  days'  work  will  pay  for  10  cords  of 
wood,  at  3  dollars  a  cord,  what  is  the  price  of  1 
day's  labor  ? 

34.  A  man  engaged  to  labor  5  months  for  80  dol- 
lars, but  by  request  continued  3  months  longer,  at 
the  same  rate ;  what  amount  will  be  due  him  for  the 
whole  time  ? 

35.  If  you  pay  60  cents  for  some  lemons,  at  the 
rate  of  6  for  10  cents,  and  sell  them  at  the  rate  of  9 
for  20  cents,  how  many  cents  will  you  gain  by  the 
operation  ? 

36.  If  two  ships  are  120  miles  apart,  and  sail 
directly  toward  each  other,  one   at  the  rate   of  9 
miles  an  hour,  and  the  other  at  the  rate  of  11  m^es 
an  hour,  how  many  hours  before  they  will  meet  ? 


44  INTELLECTUAL   ARITHMETIC.  [23. 

S3.  Division  \s  the  process  of  finding  how  many  times 
one  number  is  contained  in  another ;  and  the  result  is  called 
the  Quotient.  The  sign  of  division  is  written  thus,  ~,  and, 
placed  between  two  numbers  or  quantities,  shows  that  the 
one  on  the  left  is  to  be  divided  by  the  one  on  the  right. 
24  ~  8  =  3  shows  that  24  divided  by  8  is  equal  to  3. 

1.  How  many  times    9  are  6  times    6  ? 

2.  How  many  times    4  are  5  times    8  ? 

3.  How  many  times    8  are  6  times  12  ? 

4.  How  many  times  10  are  5  times  20  ? 

5.  How  many  times  15  are  3  times  25  ? 

6.  How  many  times  20  are  10  times  12  ? 

7.  How  many  times  16  are  8  times    8  ? 

8.  How  many  times  28  are  7  times  16  ? 

9.  How  many  times  25  are  5  times  30  ? 

10.  How  many  times  20  are  12  times  10  ? 

11.  16  times    4  are  how  many  times    8  ? 

12.  9  times  12  are  how  many  times    6  ? 

13.  8  times  14  are  how  many  times  16  ? 

14.  4  times  42  are  how  many  times  12  ? 

15.  7  times  18  are  how  many  times    9  ? 

16.  14  times  10  are  how  many  times  28  ? 

17.  12  times    8  -j-    4  are  how  many  times  10  ? 

18.  6  times  15  -j-  20  are  how  many  times  12  ?  * 

19.  How  many  times  9  +  3  are  7  times  13  less  10  ? 

20.  How  many  times  18  —  4  are  8  times  12  +  2  ? 

21.  In  8  X  12,  how  many  times  64  -=-  8  ? 

22.  In  6  X  20  +  12,  how  many  times  55  -r-  5  ? 

23.  In  48  +  24  divided  by  6,  how  many  times  4  ? 

24.  How  many  times  12  —  7  are  9  times  8  ? 

25.  How  many  times  9  +  6  in  6  times  12  +  3  ? 

26.  How  many  times  27  -f-  9  +   7x3  are  8  X 
11  +  20  ? 

*  Each  sign  affects  only  the  number  placed  after  it.     When  there  is  a 
remainder  in  the  result,  let  it  simply  be  mentioned  as  such. 


24.]  INTELLECTUAL   ARITHMETIC.  45 

24.  1.  How  many  vests,  at  5  dollars  each,  will 
pay  for  7  weeks'  board,  at  6  dollars  a  week,  and  18 
dollars  borrowed  money  ? 

2.  If  a  man  receive  16  pounds  of  sugar  in  ex- 
change for  20  pounds  of  cheese  at  8  cents  a  pound, 
what  is  the  price  of  the  sugar  per  pound  ? 

3.  James  paid  36  cents  for  some  oranges  at  3 
cents  apiece,  and,  after  eating  5  of  them,  he  gave 
the  remainder,  at  4  cents  apiece,  for  a  knife  ;  how 
much  did  the  knife  cost  him  ? 

4.  Omar  bought  30  peaches  at  the  rate  of  2  for  3 
cents,  and,  after  eating  3  of  them  and  giving  3  to 
his  brother,  he  sold  the  remainder  at  the  rate  of  3 
for  7  cents  ;  did  he  gain  or  lose  by  the  bargain,  and 
how  much  ? 

5.  A  farmer  sold  9  sheep  at  12  shillings  a  head, 
and  11  bushels  of  oats  at  2  shillings  a  bushel ;  how 
many  yards  of  cloth,  at  10  shillings  a  yard,  will  pay 
the  debt  ? 

6.  If  I  buy  40  turkeys  at  the  rate  of  5  for  3  dol- 
lars, and  sell  them  at  the  rate  of  8  for  7  dollars,  how 
much  will  I  gain  by  the  operation  ? 

7.  If  a  drover  buy  24  lambs  for  30  dollars,  at  how 
much  must  he  sell  them  a  head  to  gain  18  dollars  on 
the  cost  ? 

8.  If  5  men  ouy  a  mowing  machine  for  120  dol- 
lars, and  rent  it  3  weeks  for  15  dollars  a  week,  and 
then  sell  it  for  100  dollars,  what  is  each  man's  share 
of  the  gain  ? 

9.  If  5  barrels  of  flour  are  worth  30  dollars,  how 
many  yards  of  cloth  worth  3  dollars  a  yard  will  2 
barrels  of  the  flour  buy  ? 

10.  Four  men  agree  to  build  120  rods  01  wall  for 
48  dollars,  and  to  share  equally ;  but  when  the  wall 
is  half  built,  2  men  quit,  and  the  others  finish  it ; 
how  many  dollars  must  each  receive  ? 


46  INTELLECTUAL   ARITHMETIC. 

11.  How  many  sheep  can  I  buy  for  75  dollars  at 
the  rate  of  3  for  7  dollars,  and  have  12  dollars  left  ? 

12.  A  man,  having  80  dollars,  bought  9  cords  of 
wood  at  4  dollars  a  cord,  3  barrels  of  flour  at  8  dol- 
lars a  barrel,  and  the  remainder  he  expended  for 
cloth  at  4  dollars  a  yard  ;  how  many  yards  of  cloth 
did  he  buy  ? 

13.  If  4  bushels  of  wheat  are  worth  12  bushels  of 
corn,  how  many  bushels  of  corn  are  equal  in  valuo 
to  10  bushels  of  wheat  ? 

14.  If  12  bushels  of  wheat  make  3  barrels  of  flour, 
how  many  bushels  of  wheat  will  make  7  barrels  ? 

15.  A  cistern  holding  140  gallons  has  a  pipe  by 
which  30  gallons  will  run  into  the  cistern  in  one 
hour,  and  another  that  will  discharge  20  gallons  in 
an  hour  ;  when  both  are  running,  in  what  time  will' 
the  cistern  be  filled  ? 

16.  If  a  quantity  of  provision  serve  7  men  12 
days,  how  long  would  it  serve  4  men  ? 

17.  A  merchant  bought  15  bushels  of  clover  seed 
for  75  dollars  ;  he  wishes  to  keep  3  bushels  for  his 
own  use,  and  to  sell  the  remainder  so  as  to  make  9 
dollars  on  the  first  cost  of  the  whole  ;  how  much 
must  he  ask  a  bushel  ? 

18.  A  man  bought  a  span  of  horses  for  80  dollars 
each  ;  he  spent  40  dollars  in  fitting  them  for  market, 
and  then  sold  them  for  800  dollars  ;  what  was  his 
gain  on  each  horse  ? 

19.  A  tailor  bought  15  yards  of  one  kind  of  cloth 
for  60  dollars,  and  25  yards  of  another  kind  for  75 
dollars  ;  what  was  the  difference  in  the  price  per 
yard  ? 

20.  A  thief,  having  36  miles  the  start  of  an  officer, 
travels  at  the  rate  of  6  miles  an  hour  ;  the  officer 
pursues  at  the  rate  of  9  miles  an  hour ;  in  how  many 
hours  will  he  overtake  the  thief  ? 


84.]  INTELLECTUAL   ARITHMETIC.  47 

21.  Add  5  to  22,  divide  the  sum  by  9,  multiply 
the  quotient  by  12,  subtract  6  from  the  product,  and 
add  10  to  the  remainder  ;  what  will  be  the  result  ? 

22.  Divide  40  by  8,  multiply  the  quotient  by  9, 
to  the  product  add  11,  from  the  sum  take  6,  and 
what  will  remain  ? 

23.  Multiply  20  by  4,  subtract  40,  add  10,  divide 
by  5,  multiply  by  7,  and  what  is  the  result  ? 

24.  Prom  36  subtract  6,  divide  the  remainder  by 
5,  multiply  the  quotient  by  12,  add  15  to  the  product, 
subtract  77  from  the  sum,  divide  the  remainder  by 
10,  and  what  will  be  the  quotient  ? 

25.  Add  5  and  7  to  8,  multiply  the  sum  by  3, 
from  the  product  subtract  5,  divide  the  remainder 
by  11,  multiply  the  quotient  by  6,  add  20  to  the 
product,  and  what  will  be  the  sum  ? 

26.  Subtract  10  from  6  multiplied  by  8,  to  the 
remainder  add  4,  divide  the  sum  by  6,  multiply  the 
quotient  by  11,  subtract  7  from  the  product,  divide 
the  remainder  by  10,  add  30  to  the  quotient,  and 
what  will  be  the  sum  ? 

27.  Multiply  15  by  5,  add  5,  divide  by  8,  multiply 
by  6,  subtract  10,  divide  by  5,  add  2,  multiply  by  11, 
and  what  will  be  the  product  ? 

28.  10  +  8-f-6x9  —  7x5  + 20 -MO +  8  = 
how  many  ? 

29.  8x9-7- 12 +  8x5  + 10 -Ml  x8  + 20 -r 
12  +  4  X  7  —  3  =  how  many  ? 

30.  25  —  5-7-2x9  +  10-7-20x12  +  15  —  5 
--  7  +  8  +  2  =  how  many  ? 

31.  36-7-9x12  +  8-7-7x5+10  —  25-7^5  + 
4x9  —  11  -MO  X  6  -T-  3  =  how  many  ? 

NOTE.  The  above  examples  will  afford  a  thorough  and  profitable 
mental  drill  to  the  pupil,  and  also  familiarize  the  signs  and  terms  used 
in  the  preceding  pages,  and  which  must  be  well  understood  in  the  com- 
mencement of  the  study  of  Written  Arithmetic.  The  teacher  can  extend 
the  number  of  examples  at  pleasure. 


48  INTELLECTUAL   ARITHMETIC. 

CHAPTER  V. 
REDUCTION. 

25.     TABLE  OF  UNITED  STATES  MONEY. 

10  mills  (m.)  make  1  cent,  c. 

10  cents  "  1  dime,  d. 

10  dimes  "  1  dollar,  9. 

10  dollars  "  1  eagle,  E. 

NOTE.  Dollars  and  cents  are  separated  by  a  period  (.) ;  thus,  $2.10,  ig 
read  2  dollars  10  cents. 

A  Simple  Number  contains  but  one  name  or  denomina- 
tion ;  thus,  5, 84, 12  bushels,  65  dollars,  are  simple  numbers. 

A  Compound  Number  contains  two  or  more  names  or 
denominations ;  thus,  5  dollars  25  cents,  16  bushels  3  pecks, 
3  days  10  hours,  are  compound  numbers. 

Reduction  is  the  process  of  changing  numbers  from  one 
denomination  to  another,  without  altering  their  value  ;  thus, 
changing  pounds  to  ounces,  ounces  to  pounds,  dollars  to 
cents,  &c.,  is  reduction. 

1.  How  many  mills  in  2  cents?  in  3  cents? 

2.  How  many  cents  in  1  dime  ?  in  3  dimes  ? 

3.  How  many  dimes  in  3  dollars?  in  4  dollars? 

4.  How  many  dollars  in  2  eagles?  in  5  eagles?          v 

5.  How  many  cents  in  4  dimes  and  7  cents? 

6.  How  many  dimes  in  3  dollars  and  6  dimes? 

7.  If  Jam3S   earned  12  dollars,   and    his   father  3 
eagles,  how  many  dollars  did  they  both  earn  ? 

8.  A  man  has  4  eagles,  4  five  dollar  bills,  and  4 
dimes  ;  how  many  dollars  and  cents  has  he  ? 

9.  How  many  dimes  are  equal  to  40^  cents?  to  70 
cents? 

10.  What  is  the  difference  in  the  cost  of  8  yards 
of  cloth  at  2  dimes  a  yard,  and  6  yards  at  30  cents  a 
yard? 


26,  37.]      INTELLECTUAL  ARITHMETIC.  49 

26.  TABLE  OF  ENGLISH  MONEY. 

-  4  farthings  (far.)         make         1  penny,       d. 
12  pence  "  1  shilling,     s. 

20  shillings  1  pound,       jE. 

NOTE.    A  sovereign  (sov.)  is  equal  in  value  to  one  pound. 

1.  How  many  farthings  in  1  penny?  in  3  pence? 
in  6  pence  ?  in  9  pence  ? 

2.  How  many  pence  in  1  shilling  ?  in  4  shillings  ? 
in  5  shillings  ?  in  9  shillings  ?  in  10  shillings  ? 

3.  How  many  pence  in  8  farthings  ?  in  24  far- 
things ?  in  48  farthings  ? 

4.  How  many  shillings  in  24  pence  ?  in  84  pence  ? 
in  108  pence  ? 

5.  How  many  pounds  in  40  shillings  ?  in  120  shil- 
lings ? 

6.  At  5  shillings  a  yard,  how  many  pounds  will 
20  yards  of  carpeting  cost  ? 

7.  At  7  shillings  a  pair,  how  many  pairs  of  shoes 
can  be  bought  for  2  sovereigns  ? 


27.  TABLE  OF  TROY  WEIGHT. 

24  grains  (gr.)       make     1  pennyweight,    pwt. 
20  pennyweights         "        1  ounce,  oz, 

12  ounces  "        1  pound,  Ib. 

1.  How  many  grains  in  2  pennyweights  ?  in  4  ? 

2.  How  many  pennyweights  in  3  ounces  ?  in  5  ? 

3.  How  many  pennyweights  in  96  grains  ?  in  124 
grains  ? 

4.  In  120  pennyweights  how  many  ounces  ?   in 
200  pennyweights  ? 

5.  What  will  a  gold  chain,  weighing  15  penny- 
weights cost,  at  8  dimes  a  pennyweight  ?  how  many 
dollars  and  cents  ? 

4 


60  INTELLECTUAL  ARITHMETIC.  [28. 

28.  TABLE  OF  AVOIRDUPOIS  WEIGHT 

16  drams  (dr.)  make  1  ounce,  oz. 

16  ounces  "  1  pound,  lb. 

100  pounds  "  1  hundred  weight,  cwt. 

20  hundred  weight       "  1  ton.  T. 

1.  How  many  drams  in  3  ounces  ?  in  4  ounces  ? 
j;i  6  ounces  ? 

2.  How  many  ounces  in  32  drams  ?  in  48  drains  ? 
in  64  drams  ? 

3.  How  many  ounces  in  3  pounds  ?  in  5  Ibs.  ?  in 
7  Ibs.  ? 

4.  How  many  ounces  in  2  Ibs.   6  oz.  ?   in  4  Ibs. 
10  oz.  ? 

5.  In  3  cwt.  and  5  Ibs.,  how  many  pounds? 

6.  In  5  pounds,  how  many  ounces  V 

7.  How  many  pounds  in  3  cwt.  ?   in  6  cwt.  ?  in 
9  cwt.  ? 

8.  In  16  tons,  how  many  cwt.  ?  in  25  tons  ? 

9.  In  1  ton  and  5  cwt.,  how  many  cwt.  ?    how 
many  pounds  ? 

10.  How  many  dollars  will  3  cwt.  of  flour  cost,  if 
25  pounds  cost  5  dimes  ? 

11.  What  will  1  ton  and  5  cwt.  of  hay  cost,  if  5 
cwt.  cost  3  dollars  ? 

12.  What  will  2  cwt.  10  Ibs.  of  beef  cost  at  6  cents 
a  pound  ? 

13.  If  8  ounces  of  tea  cost  4  dimes,  what  will  2 
pounds  cost  ? 

14.  What  will  be  the  cost  of  4  cwt.  of  sugar,  at  7 
cents  a  pound  ? 

15.  Which  will  cost  the  more,  5  cwt.  of  fish  at  6 
cents  a  pound,  or  3  tons  of  hay  at  50  cents  a  cwt.  ? 

16.  What  will  1  ton  of   hay  cost  at  1  cent  a 
pound  ? 


INTELLECTUAL  ARITHMETIC.  5l 

29.  TABLE  OF  LONG  MEASURE. 

12    inches  (in.)  make  1  foot,  ft. 

3    feet  "  1  yard,  yd. 

5£  yards,  or  16£  feet,  "  1  rod,  rd. 

40    rods  "  1  furlong,  fur. 

8    furlongs,  or  320  rods,    "  1  mile,  mi. 

3    miles  "  1  league,  lea. 

69£  miles  "  1  degree,  dcg.  or  °. 

360    degrees  "  1  circle  of  the  earth. 

1.  How  many  inches  in  3  ft.  ?  in  5  ft.  ?  in  10  ft.  ? 
in  12  ft.  ? 

2.  How  many  feet  in  4  yards  ?    in  6  yards  ?   in  9 
yards  ? 

3.  How  many  yards  in  15  feet  ?  in  24  feet  ? 

4.  How  many  yards  in  2  rods  ?  in  4  rods  ? 

5.  How  many  furlongs  in  5  miles  ?  in  7  miles  and 
4  furlongs  ? 

6.  How  many  furlongs  in  80  rods  ?   in  120  rods  ? 
in  160  rods  ? 

7.  In  2  miles  4  fur.  20  rods,  how  many  rods  ? 

8.  How  many  leagues  in  9  miles  ?  in  18  miles  ?  in 
36  miles  ? 

9.  How  many  inches  in  3  yds.  1  ft.  10  in.  ? 

10.  In   108   inches   how    many   yards  ?    in    144 
inches  ? 

11.  If  a  man  travel  5  miles  an  hour,  how  long 
will  it  take  him  to  travel  20  leagues  ? 

12.  If  a  ship  sail  20  leagues  a  day,  how  long  will 
it  take  her  to  sail  from  New  York  to  Liverpool,  it 
being  3000  miles  ? 

13.  In  100    inches   how  many    yards,  feet,  and 
inches  ? 

14.  At  8  dimes  a  foot,  how  many  dollars  will  3  yds. 
1  ft.  of  iron  railing  cost  ? 

15.  In  2  rods  5  feet?  how  many  inches  ? 


•r>"  INTELLECTUAL   ARITHMETIC.         [3O,  31. 

3O.  TABLE  OF  CLOTH  MEASURE. 

2£  inches  (in.)       make     1  nail,  na. 

4  nails  1  quarter  of  a  yard,  qr. 

4  quarters  1  yard,  yd. 

1.  How  many  nails  in  3  qrs.  ?  in  5  qrs.  ? 

2.  How  many  nails  in  2  yds.  2  qrs.  ? 

3.  How  many  quarters  in  5  yds.  ?   in  6  yds.  3 
qrs.? 

4.  How  many  yards  in  16  qrs.  ?  in  56  qrs.  ? 

5.  How  many  qrs.  in  36  nails  ?  in  64  na.  ? 

6.  How  many  qrs.  in  5  yds.  ?   in  6  yds.  ?   in  7 
yds.  ? 

7.  In  4  yards,  how  many  nails  ? 

8.  In  6  yards,  how  many  qrs.  ? 

9.  In  123  nails,  how  many  yards  ? 


31.       TABLE  OF  LAND  OR  SQUARE  MEASURE. 

144  square  inches  (sq.  in.)  make  1  square  foot,  sq.  ft. 
9  square  feet  "     1  square  yard,  sq.  yd. 

30£  square  yards  "     1  square  rod,  P. 

40  square  rods  "     1  rood,  R. 

4  roods  "     1  acre,  A. 

640  acres  "     1  square  mile,  Sq.  M. 

1.  How  many  square  feet  in  5  square  yards  ?    in 
10  square  yards  ?  in  20  square  yards  ? 

2.  How  many  square  yards  in  36  sq.  ft.  ?  in  72 
sq.  ft.  ?  in  108  sq.  ft.  ? 

3.  How  many  square  rods  in  3  roods  ?  in  5  roods  ? 
in  7  roods  ? 

4.  How  many  acres  in  20  roods  ?  in  80  roods  ? 

5.  At  4  dollars  a  square  rod,  what  would  2  roods 
10  rods  of  land  cost  ? 


32.  33.]      INTELLECTUAL  ARITHMETIC.  £3 

32.  TABLE  OP  CUBIC  MEASURE. 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot,  cu.  ft. 
27      "     feet  "     1  cubic  y ard,  cu.  yd. 

24f   "     feet  "     1  perch  of  stone,Pch. 

16     "     feet  "     1  cord  foot,    c.  ft. 

8  cord  feet  or  j  u     l  *    d   f        d  0 

128  cubic  feet      \ 

1.  How  many  cubic  feet  in  2  cubic  yards?  in  3 
cubic  yards  ? 

2.  How  many  cubic  feet  in  2  perch  of  stone  ?  in 
4  perch  ?  in  6  perch  ? 

3.  How  many  cord  feet  in  3  cords  of  wood  ?  in  7 
cords  ?  in  9  cords  ? 

4.  How  many  cord  feet  in  120  cubic  feet  of  wood  ? 
in  200  cubic  feet  ? 

5.  How  many  cords  in  24  cord  feet?  in  56  cord 
feet? 


33.  TABLE  OF  LIQUID  MEASURE. 

4    gills  (gi.)  make  1  pint,  pt. 

2    pints  "  1  quart,  qt. 

4    quarts  "  1  gallon,  gal. 

311-  gallons  "  1  barrel,  bar. 

2    barrels,  or  63  gallons  "  1  hogshead,  hhd. 

1.  How  many  gills  in  4  pints  ?  in  6  pints  ?  in  10 
pints  ? 

2.  How  many  pints  in  3  quarts  ?  in  8  quarts  ?  in 

1  gallon  ?  in  3  gallons  ? 

3.  How  many  gills  in  4  quarts  ?  in  6  quarts  ?  in 
8  quarts  ? 

4.  How  many  quarts  in  3  gallons?    how  many 
pints  ?   how  many  gills  in  3  quarts  ?  in  1  gallon  and 

2  quarts  ? 

5* 


54  INTELLECTUAL   ARITHMETIC.  [84. 

5.  How  many  gills  in  2  gallons  2  qts.  ? 

6.  How  many  quart  cups  could  be  filled  from  a 
10  gallon  keg  of  wine  ?  how  many  pint  bottles  ? 

7.  In  48  gills,  how  many  pints  ?  quarts  ? 

8.  How  many  gallons  in  64  gills  ?  in  96  gills  ? 

9.  How  many^quarts  in  56  pints  ?  gallons  ? 

10.  In   10   gallons,   how   many   quarts?    pints? 
gills? 

11.  What  will  be  the  cost  of  6  gallons  of  burning 
fluid,  at  15  cents  a  quart  ? 

12.  If  a  pint  of  molasses  cost  7  cents,  what  will  a 
gallon  cost  ? 

13.  If  one  gallon  of  oil  cost  90  cents,  what  will  3 
gallons  and  2  quarts  cost  ? 

14.  If  you  should  draw  10  gallons  and  8  quarts 
from  a  hogshead  of  molasses,  how  much  would  re- 
main ? 


34.  TABLE  OF  DRY  MEASURE. 

2  pints  (pt.)  make     1  quart,  qt. 

8  quarts  "        1  peck,  pk. 

4  pecks  "        1  bushel  bu. 

1.  How  many  pints  in  1  peck  ?  in  2  pks.  4  qts.  ? 

2.  How  many  quarts  in  1  bu.  2  pks.  ? 

3.  In  2  bu.  1  pk.  6  qts.  how  many  quarts  ? 

4.  In  64  quarts  how  many  pecks  ?  bushels  ? 

5.  In  80  pints  how  many  pecks  ? 

6.  At  3  cents  a  pint,  what  will  be  the  cost  of  one 
peck  of  chestnuts  ? 

7.  If  one  bushel  of  hickory  nuts  cost  160  cents, 
what  will  be  the  cost  of  6  quarts  ? 

8.  Bought  2  pecks  of  cranberries  for  96  cents,  and 
Bold   them  for  5  cents  a  pint;   how  much  was  the 
gain  ? 


INTELLECTUAL   ARITHMETIC. 


55 


35. 


TABLE  OF  TIME. 


60  seconds  (sec.) 
60  minutes 
24  hours 

7  days 
12  calendar  months 

365  days 

366  days 
100  years 


make  1  minute,  m. 

"  1  hour,  hr. 

"  1  day,  d. 

"  1  week,  w. 

"  1  year,  yr. 

"  1  common  year,      yr. 

"  1  leap  year,  yr. 

"  1  century,  C. 


The  divisions  of  the  year,  the  names  of  the  months, 
and  the  number  in  each,  are  shown  in  the  following 
table :  — 


Winter. 

(  1st       month 
2d 

,  January 
February 

has 

44 

31 

28* 

days. 

u 

(3d 

44 

March 

44 

31 

u 

Spring. 

{4th 

44 

April 

44 

30 

u 

(5th 

44 

May 

44 

31 

M 

(6th 

44 

June 

44 

30 

a 

Summer. 

{7th 

44 

July 

44 

31 

a 

(8th 

44 

August 

44 

31 

u 

(9th 

44 

September 

44 

30 

a 

Autumn. 

{  10th 

44 

October 

44 

31 

a 

(  llth 

44 

November 

44 

30 

u 

Winter. 

12th 

44 

December 

44 

31 

u 

The  following  lines  will  help   to   remember  the 
number  of  days  in  each   month  :  — 

Thirty  days  hath  September, 
April,  June,  and  November; 

AIL  the  rest  have  thirty-one, 

Save  February,  which  alone 
Hath  twenty-eight;  and  one  day  more 
We  add  to  "it,  one  year  in  four. 

*  In  leap-year,  29, 


66 


INTELLECTUAL   ARITHMETIC. 


[36. 


1.  How  many  seconds  in  2  minutes  ?  in  5  minutes  ? 

2.  How   many   seconds   in   10   minutes  ?    in   20 
minutes  ? 

3.  How  many  seconds  in  1  hour  ?  in  2  hours  ? 

4.  How  many  minutes  in  3  hours  ?  in  5  hours  ? 

5.  How  many  hours  in  2  days  ?  in  3  days  ? 

6.  In  2  days  and  12  hours  how  many  hours  ? 

7.  In  6  weeks  how  many  days  ?  in  9  weeks  ? 

8.  How  many  weeks  in  49  days  ?  in  84  days  ? 

9.  How  many  weeks  and  days  in  75  days  ?  in  90 
days? 

10.  How  many  hours  in  3  days  10  hours  ? 

11.  In  36  months  how  many  years  ?  in  84  months? 

12.  How  many  days  from  January  1st  to  March 
10th,  inclusive  ? 

13.  How  many  days  from  April  10th  to  the  15th 
of  June  ? 


36. 


MISCELLANEOUS  TABLE. 


12  units 

make  1  dozen. 

12  dozen 

"     1  gross. 

12  gross 

"     1  great  gross. 

20  units 

"     1  score. 

24  sheets  of  paper 

"     1  quire. 

20  quires 

"     1  ream. 

56  pounds  . 

"     1  bushel  of  corn. 

60  pounds 

"     1  bushel  of  wheat. 

196  pounds 

"     1  barrel  of  flour. 

200  pounds 

u  (  1  barrel  of  beef,  p 
1      or  fish. 

1.  What  cost  1  ream  of  paper,  at  20  cents  a  quire  ? 

2.  What  cost  3  dozen  lemons,  at  3  cents  apiece  ? 

3.  What  cost  2  gross  of  pens,  at  5  cents  a  dozen  ? 

4.  At  7  dollars  a  hundred  pounds,  what  will  2 
barrels  of  pork  cost  ? 


37.]  INTELLECTUAL   ARITHMETIC.  57 

CHAPTER  VI. 
FRACTIONS. 

37.  1.  WHAT  is  understood  by  one  half,  one 
third,  one  fourth,  one  fifth,  &c.  ? 

ANS.  When  a  number  or  thing,  as  a  unit  or  an 
apple,  is  divided  into  two  equal  parts,fc  each  of  the 
parts  is  called  one  half;  when  into  three  equal  parts, 
each  of  the  parts  is  called  one  third ;  two  of  the  parts 
are  called  two  thirds,  &c. 

2.  How  many  halves  in  1  ? 

3.  How  many  thirds  in  1  ? 

4.  If  a  peach  be  divided  into  2  equal  parts,  what 
is  each  part  called  ? 

5.  If  an  orange  be  divided  into  3  equal  parts, 
what  are  the  parts  called  ? 

6.  How  many  halves  in  4? 

ANALYSIS.  Since  in  1  there  are  2  halves,  in  4  there  are  4 
times  2  halves,  or  8  halves.  Therefore  there  are  8  halves  in  4. 

7.  How  many  halves  in  5  ?  in  6  ? 

8.  How  many  halves  in  7  ?  in  7  and  1  half? 

9.  How  many  thirds  in  3  ?  in  4  ?  in  5  ? 

10.  How  many  thirds  in  7  ?  in  8  ?  in  9  ? 

11.  How  many  thirds  in  6  and  1  third?  in  6  and 
2  thirds  ? 

12.  How  many  halves  in  5  ?  how  many  thirds  ? 

13.  How  many  halves  in  10  and  1  half? 

14.  How  many  thirds  in  9  and  2  thirds  ? 

15.  In  8  halves  how  many  whole  things  ? 

ANALYSIS.  Since  in  2  halves  there  is  one  ivhole  thing, 
in  8  halves  there  are  as  many  whole  things  as  2,  the  num- 
ber of  halves  in  \,  is  contained  times  in  8,  which  is  4 
times.  Therefore,  in  8  haloes  there,  are  4  whole  things. 


58  INTELLECTUAL   ARITHMETIC.  [37. 

16.  How  many  whole  things  in  12  halves  ?  in  16 
halves  ?  in  24  halves  ? 

17.  How  many  whole  things  in  9  thirds?  in  18 
thirds  ? 

18.  How  many  whole  things  in  10  halves?  in  12 
thirds  ?  in  21  thirds  ?  in  20  halves  ? 

19.  How  many  half  bushels  in  3  bushels  and  1 
half? 

20.  John  gave  6  peaches  to  his  2  brothers ;  what 
part  of  them  did  each  have  ? 

21.  What  is  1  half  of  6  ? 

ANALYSIS.  It  is  that  number  which  taken  2  times 
loill  make  G  ;  2  times  3  is  G.  Therefore  3  is  1  half 
0/6. 

22.  What  is  1  third  of  9  ?  of  18  ?  of  27  ?  of  36  ? 

23.  What  is  1  half  of  8  ?  of  12  ?  of  18  ?  of  22  ? 

24.  How  can  you  take  1  half  of  an  orange  ?  1  third  ? 

25.  How  can  you  take  2  thirds  of  an  apple  ? 

26.  Will|am  had  30  new  pennies,  and  John  had 
1  half  as  many  ;  how  many  had  John  ? 

27.  If  a  pound  of  candles  cost  15  cents,  what  will 
1  third  of  a  pound  cost  ?  2  thirds  ? 

28.  George  is  12  years  old,  and  Mary  is  2  thirds 
as  old  as  he  ;  how  old  is  Mary  ? 

29.  If  a  barrel  of  flour  cost  10  dollars,  and  a 
barrel  of  cider  1  half  as  much,  what  is  the  cost  of 
the  cider  ? 

30.  If  3  tons  of  hay  cost  27  dollars,  what  part  of 
27  dollars  will  1  ton  cost  ?  2  tons  ? 

31.  A  boy,  having  33  cents,  spent  2  thirds  of  them ; 
how  many  had  he  left  ? 

32.  Edwin  gave  2  peaches  and  1  half  to  his  sister, 
and  1  peach  and  1  half  to  his  brother ;  how  many 
peaches  did  he  give  to  both  ? 

33.  A  farmer,  having  44  sheep,  sold  1  half  of  them ; 
how  many  had  he  left  ? 


38.]  INTELLECTUAL   ARITHMETIC.  59 

38.     1.    What  do  you  understand  by  1  fourth? 
3  fourths  ? 

2.  What  do  you  understand  by  1  fifth  ?  2  fifths  ? 
3  fifths?  4  fifths? 

3.  What  do  you  understand  by  1  sixth  ?  3  sixths? 
5  sixths  ? 

4.  How  can  you  take  1  fourth  of  any  thing  ?  1 
sixth  ? 

5.  How  can  you  take  3  fourths  of  any  thing  ?  3 
fifths  ? 

6.  How  many  fifths  in  1  ?  in  4  ?  in  6  ? 

7.  How  many  fourths  in  1  ?  in  2  and  3  fourths  ? 

8.  How  many  sixths  in  2  ?  in  3  and  4  sixths  ? 
.     9.   In  4  and  5  sixths  how  many  sixths  ? 

10.  In  8  and  3  fourths  how  many  fourths  ? 

11.  In  7  and  4  fifths  how  many  fifths  ? 

12.  Which  is  greater,  1  fourth  or  1  fifth  ?  1  fifth 
or  1  sixth  ? 

13.  How  many  times  1  in  8  fourths  ?  in  16  fourths  ? 

14.  How  many  times  1  in  15  fifths  ?  in  25  fifths  ? 

15.  How  many  times  1  in  24  sixths  ?  in  36  sixths? 

16.  What  is  1  fourth  of  12  ?  of  20  ?  of  28  ? 

17.  What  is  1  sixth  of  18  ?  of  30  ?  of  42  ? 

18.  What  is  1  fourth  of  32  ?  of  40  ?  of  48  ? 

19.  What  is  1  fifth  of  10  ?  of  20  ?  of  50  ? 

20.  What  is  1  sixth  of  36  ?  2  sixths  ?  5  sixths  ? 

21.  What  is  1  fifth  of  40  ?  3  fifths  ?  4  fifths  ? 

22.  What  is  3  fourths  of  16  ?  of  24  ? 

23.  What  is  2  fifths  of  10  ?  of  25  ? 

24.  What  is  3  sixths  of  30  ?  5  sixths  of  42  ? 

25.  If  a  ton  of  hay  cost  12  dollars,  what  will  1 
fourth  of  a  ton  cost  ?  2  fourths  ?  3  fourths  ? 

26.  If  5  bushels  of  apples  cost  90  cents,  what  part 
of  90  cents  will  1  bushel  cost  ?  2  bushels  ?  3  bushels  ? 

27.  When  coal  is  6  dollars  a  ton,  what  part  of  a 
ton  can  be  bought  for  1  dollar  ?  for  2  dollars  ?  for  5 
dollars  ? 


GO  INTELLECTUAL   ARITHMETIC.  [38, 

28.  Bought  a  piece  of  land  for  45  dollars ;  what 
is  1  fifth  of  it  worth  ?  2  fifths  ?  3  fifths  ? 

29.  If  you  pay  30  dollars  for  one  month's  labor, 
what  do  you  pay  for  1  fifth  of  a  month  ?  for  1  sixth  ? 
t>r  5  sixths  ?  for  4  fifths  V 

30.  A  man   divided   48   cents  equally  among  6 
beggars ;  what  part  of  the  whole  did  each  beggar 
receive  ?  what  part  did  2  receive  ?  3  ?  4  ?  5  ? 

31.  If  in  a  basket  of  54  eggs  1  sixth  are  bad,  how 
many  are  good  ? 

32.  If  a  man  earn  15  dollars  a  week,  and   spend 

2  fifths  of  it,  how  much  does  he  save  ? 

33.  A  drover,  having  GO  sheep,  sold  1  fourth  of 
them  at  one  time,  and  1  fifth  at  another ;  how  many 
had  he  left  ? 

34.  Rollin  had  18  marbles,  and  gave  2  sixths  of 
them  to  Martin  ;  how  many  did  he  give  Martin,  and 
how  many  did  he  keep  for  himself? 

35.  If  Harry  bought  6  pounds  of  coffee  for  1  dol- 
lar, what  part  of  1  dollar  did  1  pound  cost  ?  2  pounds  ? 

3  pounds  ?  4  pounds  ? 

36.  When  tea  is  5  shillings  a  pound,  what  part  of 
a  pound  can  be  bought  for  1  shilling  ?  2  shillings  ? 
3  shillings  ?  4  shillings  ? 

87.    If  a  barrel  of  pork  cost  15  dollars,  what  will 
2  thirds  of  it  cost  ?  3  fifths  ? 

38.  A  gentleman  is  60  years  old,  and  his  wife  is  4 
fifths  as  old  ;  how  old  is  she  ? 

39.  Andrew  is  18  years  old,  and  his  sister,  Jane,  is 
5  sixths  as  old  ;  how  old  is  Jane  ? 

40.  Paid  36  dollars  for  1  acre  of  land ;  what  is  1 
sixth  of  it  worth  ?  3  sixths  ?  1  fourth  ?  3  fourths  ? 

41.  If  you  divide  a  barrel  of  flour  equally  among 
5  poor  families,  what  part  of  the  barrel  will  1  family 
receive  ?  2 -families  ?  3  families  ?  4  families  ?  5  fam- 
ilies ? 


39. J  INTELLECTUAL   ARITHMETIC.  61 

39.     1,    What  do  you  understand  by  1  seventh  ? 

3  sevenths  ?  4  sevenths  ?  5  sevenths  ? 

2.  What  is  meant  by  1  eighth?    5  eighths?   1 
ninth  ?  3  ninths  ?  5  ninths  ?  7  ninths  ? 

3.  What  is   meant   by   3   tenths?    9   tenths?    5 
twelfths  ?  11  twentieths  ? 

4.  How  many  ninths  in  a  unit,  or  whole  thing  ? 
how  many  tenths  ?  how  many  elevenths  ?  how  many 
twelfths  ?  how  many  twentieths  ? 

5.  How  many  times  1  in  14   sevenths  ?    in   32 
eighths  ?  in  45  ninths  ? 

6.  How  many  times  1  in  70  tenths  ?  in  44  elevenths  ? 
in  30  fifteenths  ?  in  80  twentieths  ? 

7.  What  is  1  seventh  of  42  ?  of  63  ?  of  84  ? 

8.  What  is  1  eighth  of  24  ?  of  56  ?  of  64  ? 

9.  What  is  1  ninth  of  36  ?  3  ninths  ?  7  ninths  ? 

10.  What  are  3  tenths  of  50  ?  of  60  ?  of  90  ? 

11.  What  is  1  twelfth  of  72  ?  5  twelfths  ?  7  twelfths  ? 

12.  What  is  1  twentieth  of  60  ?  14  twentieths  ? 

13.  How  many  times  1  in  19  eighths  ?  in  40  ninths  ? 
in  65  twelfths  ? 

14.  How  many  times  1  in  28  sevenths  ?   in  56 
tenths  ?  in  52  elevenths  ? 

15.  In  3  and  5  sevenths  how  many  sevenths  ? 

16.  In  6  and  3  eighths  how  many  eighths  ? 

17.  In  8  and  7  ninths  how  many  ninths  ? 

18.  In  9"  and  3  twelfths  how  many  twelfths  ? 

19.  In  7  and  9  tenths  how  many  tenths  ? 

20.  If  10  pounds  of  sugar  cost  80  cents,  what  part 
of  80  cents  will  3  pounds  cost  ?  5  pounds  ? 

21.  If  a  man  earn  72  dollars  in  1  month,  how 
much  will  he  earn  in  1  fourth  of  a  month  ?  5  sixths  ? 

4  ninths  ?  7  eighths  ?  5  twelfths  ? 

22.  What  is  the  difference  between  7  eighths  of 
64  and  5  ninths  of  81  ? 

6 


62  INTELLECTUAL   ARITHMETIC.  [39. 

23.  What  will  5  eighths  of  a  bushel  of  chestnuts 
cost  at  10  cents  a  quart  ? 

24.  What  will  be  the  cost  of  4  sevenths  of  14 
dozen  of  eggs  at  11  cents  a  dozen  ? 

25.  If  James  has  108  cents,  and  Henry  has  7 
twelfths  as  many    and    20  cents  more,  how  many 
cents  has  Henry  V 

26.  What  will  be  the  cost  of  1  ninth  of  a  hogs- 
head of  molasses  at  12  cents  a  quart  ? 

27.  Meiizo,  having  48  dollars,  gave  1  sixteenth  of 
his  money  for  a  hat,  3  eighths  for  a  coat,  and  3 
twelfths  for  some  books  and  a  quarter's  tuition ;  how 
many  dollars  had  he  left  ? 

28.  A  man  bought  a  horse   for  120   dollars;  he 
gave  7  tenths  as  much  for  a  carriage  as  he  paid  for 
the  horse,  and  3  sevenths  as  much  for  a  harness  as 
he  paid  for  the  carriage ;  how  much  did  the  whole 
cost  him  ? 

29.  If  a  man   put  200  dollars   at    interest,  and 
receive  3  twentieths  of  it  annually  for  its  use,  how 
many  dollars  does  he  receive  ? 

30.  If  a  vessel  sail  12  miles  an  hour,  how  many 
times  9  miles  will  she  sail  in  3  eighths  of  a  day  ? 

31.  Abel  has  49  marbles,  and  Alonzo  has  6  sevenths 
as  many  wanting  10  ;  how  many  has  Alonzo  ? 

32.  A  man,  having  300  cedar  posts,  sold  2  fifths 
of  them  to  A,  1  sixth  to  B,  3  tenths  to  G,  and  40 
posts  to  D  ;  how  many  had  he  left  ? 

33.  What  will  be  the  cost  of  a  gold  watch  weigh- 
ing 1  third  of  a  pound  at  1  dollar  a  pennyweight  ? 

34.  What  will  be  the  cost  of  3  eighths  of  2  gallons 
of  wine  at  40  cents  a  pint  ? 

35.  A  grocer  bought  27  dozen  of  eggs  for  240 
cents,  and   sold   5  ninths  of  them  for  12  cents  a 
dozen,  and  the  remainder  for  10  cents  a  dozen ;  how 
much  did  he  gain  by  the  operation  ? 


4O.]  INTELLECTUAL   ARITHMETIC.  65 

4O.     1.    9  is  1  fourth  of  what  number  ? 

ANALYSIS.     9  is  1  fourth  of  4  times  9  ;  4  times  9  is 
36.     Therefore  9  is  1  fourth  of  36. 

2.  7  is  1  fifth  of  what  number  ? 

3.  10  is  1  eighth  of  what  number  ? 

4.  12  is  1  tenth  of  what  number  ? 

5.  20  is  1  half  of  what  number  ? 

6.  15  is  1  fourth  of  what  number  ? 

7.  30  is  1  sixth  of  what  number  ? 

8.  9  is  1  twelfth  of  what  number  ? 

9.  5  is  1  twentieth  of  what  number  ? 

10.  11  is  1  seventh  of  what  number  ? 

11.  9  times  4, and  3  fourths  of  4  are  how  many  ? 

12.  6  times  9,  and  7  ninths  of  9  are  how  many  ? 

13.  10  times  12,and  5  twelfths  of  12  are  how  many  ? 

14.  14  times  2, and  1  half  of  2  are  how  many  ? 

15.  8  times  ll,and  7  elevenths  of  11  are  how  many  ? 

16.  5  times  20,  and  13  twentieths  of  20  are  how 
many  ? 

17.  64  are  how  many  times  8  ?  5  ?  12  ? 

18.  47  are  how  many  times  9  ?  10  ?  8  ?  6  ? 

19.  81  are  how  many  times  8  ?  9  ?  11  ?  12  ? 

20.  35  are  how  many  times  7  ?  6  ?  8  ?  9  ? 

21.  75  are  how  many  times  5  ?  6  ?  7  ?  9  ?  25  ? 

22.  3  fourths  of  16  are  how  many  times  6  ? 

ANALYSIS.  3  fourths  of  16  are  as  many  times  6  as  6 
is  contained  times  in  3  times  \  of  16  ;  1  fourth  of  16 
is  4,  and  3  times  4  is  12  ;  6  is  contained  in  12,  2  times. 
Therefore  3  fourths  oflQ  are  2  times  6. 

23.  6  tenths  of  100  are  how  many  times  5  ? 

24.  5  twelfths  of  72  are  how  many  times  3  ?  4  ? 
6?  8? 

25.  7  ninths  of  63  —  3   eighths  of  24  are  how 
many  times  4  ?  5  ?  6  ?  7  ?  8  ? 

26.  11  twentieths  of  80  +  7  fifteenths  of  45  are 
how  many  times  6  ?  7  ?  9  ?  12  ?  13  ? 


64  INTELLECTUAL   ARITHMETIC.  [41. 

41.  1.  If  1  fourth  of  a  yard  of  cloth  cost  12 
cents,  what  will  1  yard  cost  ? 

ANALYSIS.  Tf  I  fourth  of  a  yard  cost  12  cents,  4 
fourths,  or  1  yard,  will  cost  4  times  12  cents  ;  4  times 
12  cents  are  48  cents.  Therefore,  if  1  fourth  of  a  yard 
cost  12  cents,  1  yard  will  cost  48  cents. 

2.  If  1  fifth  of  a  pound  of  tea  cost  10  cents,  what 
will  1  pound  cost  ? 

3.  If  1  third  of  a  gallon  of  molasses  cost  20  cents, 
what  will  1  gallon  cost  ? 

4.  20  is  1  third  of  what  numher  ? 

5.  10  is  1  fifth  of  what  number  ? 

G.  If  1  half  of  a  cord  of  wood  cost  2  dollars,  what 
will  1  cord  cost  ?  what  will  2  cords  cost  ? 

7.  A  man  gave  2  shillings  for  his  dinner,  which 
was  1  twelfth  of  all  the  money  he  had  ;  how  much 
money  had  he  ? 

8.  A  drover  sold  some  sheep,  and  gained  by  the 
sale  15  dollars,  which  was  1  fourth  of  what  the  sheep 
cost  him  :  what  was  the  cost  of  the  sheep  ? 

9.  If  I  sixth  of  a  ton  of  hay  cost  3  dollars,  what 
will  3  rixths  cost  ?  5  sixths  ?  1  ton  ? 

10.  If  a  man  can  walk  6  miles  in  1  eighth  of  a 
day,  how  far  can  he  walk  in  1  day  ?  in  2  days  ?  in  3 
days  ? 

11.  James  had  40  plums,  and  divided  1  fourth  of 
them  equally  among  5  of  his  companions  ;  how  many 
did  he  give  to  each  ? 

12.  6  is  1  eighth  of  what  number  ? 

13.  15  is  1  fifth  of  what  number  ? 

14.  40  is  1  third  of  what  number  ? 

15.  1  fourth  of  40  is  how  many  times  5  ?  7  ? 

16.  1  sixth  of  90  is  how  many  times  4  ?  5  ?  6  ? 

17.  I  have  16  dollars,  which  is  1  third  of  what  I 
paid  for  12  sheep  ;  how  much  did  I  pay  a  head  ? 


INTELLECTUAL   ARITHMETIC.  65 

18.  A  man   plowed   36    acres    of  his    farm;    3 
fourths  of  this  was  just  equal  to  1  third  of  the  whole 
number  of  acres  in  his  farm ;  how  many  acres  in  his 
farm  ? 

19.  A  pole  stands  12  feet  in  the  water,  which  is  1 
fifth  of  the  length  of  the  pole  ;  how  long  is  the  pole  ? 

20.  Bought  a  watch  and  chain ;  for  the  chain  I 
gave  15  dollars,  which  was  1  fourth  of  what  I  paid 
for  the  watch  ;  what  did  they  both  cost  me  ? 

21.  If  1  twelfth  of  an  acre  of  land  cost  5  dollars, 
what  will  2  acres  cost  ? 


42.  1.  If  3  fourths  of  a  barrel  of  flour  cost  6 
dollars,  what  will  one  barrel  cost  ? 

ANALYSIS.  If  3  fourths  of  a  barrel  of  flour  cost  6 
dollars,  1  barrel  will  cost  4  times  1  third  of  6  dollars  ; 
\  third  of  6  dollars  are  2  dollars,  and  4  times  2  dollars 
are  8  dollars.  Therefore,  <&c. 

2.  If  4  fifths  of  a  barrel  of   ale  cost  8  dollars, 
what  will  1  barrel  cost? 

3.  If  5  ninths  of  a  month's  wages  amount  to  25 
dollars,  what  will  a  month's  wages  amount  to  ?    2 
months'  ? 

4.  What  will  1  barrel  of  flour  cost,  if  5  sevenths 
of  a  barrel  cost  10  dollars  ? 

5.  Sold  a  cow  for  25  dollars,  which  was  5  fourths 
of  what  she  cost  me ;  what  did  she  cost  me  ? 

6.  Bought  4  barrels  of  vinegar   at  6   dollars   a 
barrel,  which  was  but  3  ninths  of  its  real  value  ;  what 
was  its  real  /alue  per  barrel  ? 

7.  A  speculator  bought  some  pork  for  90  dollars, 
which  was  9  elevenths  of  what  he  sold  it  for ;  how 
much  did  he  gain  ? 

5 


66  INTELLECTUAL  ARITHMETIC. 

8.  A  tailor  bought  two  pieces  of  cloth,  the  shorter 
piece  containing  24  yards ;  5  eighths  the  numoer  of 
yards  in  the  shorter  piece  is  20  yards  less  than  the 
number  of  yards  in  the  longer  piece ;    how  many 
yards  in  both  pieces  ? 

9.  If  7  tenths  of  an  acre  of  land  yield  28  bush- 
els of  wheat,  what  will  1  acre  yield  ?  what  will  3 
acres  yield  ? 

10.  16  is  4  fifths  of  what  number  ? 

ANALYSIS.  1C  is  4  ffths  of  5  times  I  fourth  of  16  ; 
1  fourth  of  16  is  4,  and  5  times  4  is  20.  Therefore,  16 
is  4 fifths  o/20. 

11.  25  is  5  eighths  of  what  number  ? 

12.  14  is  7  twelfths  of  what  number  ? 

13.  9  is  3  tenths  of  what  number  ? 

14.  12  is  4  fifteenths  of  what  number  ? 

15.  20  is  2  sevenths  of  what  number  ? 

16.  18  is  6  elevenths  of  what  number  2 

17.  21  is  3  halves  of  what  number  ? 

18.  72  is  9  eighths  of  what  number  ? 

19.  40  is  10  elevenths  of  what  number  ? 

20.  36  is  12  twentieths  of  what  number  ? 

21.  42  is  7  fifths  of  what  number  ? 

22.  5  sixths  of  24  is  2  thirds  of  what  number  ? 

ANALYSIS.  5  sixths  of  24  is  2  thirds  of  3  times  I 
half  of  5  times  1  sixth  of  24 ;  1  sixth  of  24  is  4,  and 
5  times  4  is  20;  1  half  of  20  is  10,  and  3  times  10  is 
30.  Therefore,  I  sixths  of  24  is  2  thirds  of  30. 

23.  3  fourths  of  16  is  6  sevenths  of  what  number  ? 

24.  4  fifths  of  30  is  8  elevenths  of  what  number  ? 

25.  6  fourths  of  28  is  7  ninths  of  what  number  ? 

26.  9  twelfths  of  60  is  5  thirds  of  what  number  ? 

27.  8  ninths  of  18  is  1  fourth  of  what  number  ? 

28.  11  fifteenths  of  45  is  3  halves  of  what  num. 
her. 


43.]  INTELLECTUAL   ARITHMETIC.  67 

29.  6  tenths  of  100  is  5  twelfths  of  what  number  ? 

30.  3  twentieths  of   80  is  2  sixteenths  of  what ; 
number  ? 

31.  9  eighths  of  64  is  8  fifths  of  what  number  ? 

32.  Of  a  certain  farm,  36  acres  are  woodland,  and 
5  sixths  of  the  woodland  is  3  fifths  of  the  number  of 
acres  of  cleared  land  ;   how  many  acres  of   cleared 
land,  and  how  many  acres  does  the  farm  contain  ? 

33.  Mr.  Smith  gave  5  sevenths  of  all  the  money 
lie  had  for  a  horse ;  he  then  paid  12  dollars  for  a 
saddle  and  bridle,  which  was  3  fourths  of  all  tho 
money  he  had  left ;  how  much  money  had  he  at  first  ? 

34.  A  person,  being  asked  his  age,  answered  that 
if  he  were  twice  as  old,  1  third  of  his  age  would  be 
20  years  ;  how  old  was  he  ? 


43.  A  FRACTION  is  one  or  more  of  the  equal  parts  of 
a  unit.  Fractions  are  expressed  by  figures  in  the  following 
manner,  viz. :  — 

l,  one  naif.  f ,  two  thirds. 

1,  one  third.  f ,  three  fourths, 

^,  one  fourth.  |,  seven  eighths. 

1,  one  fifth.  -j^,  nine  tenths. 

1,  one  sixth.  -J£,  eleven  twelfths. 

^,  one  seventh.  J-jJ,  thirteen  twentieths. 

|,  one  eighth.  4|,  four  and  1  seventh. 

^,  one  tenth.  9f ,  nine  and  5  eighths,  &c. 

1.  The  number  below  the  short  horizontal  line  is 
called  the  denominator. 

2.  The  number  above  the  line  is  called  the  numer- 
ator. 

3.  The  denominator  shows  into  how  many  parts 
the  whole  thing  is  divided. 


68  INTELLECTUAL  ARITHMETIC.  [43. 

4.  The  numerator  shows  how  many  of  these  parts 
are  taken  or  used. 

5.  A  proper  fraction  is  one  whose  numerator  is 
less  than  the  denominator ;  its  value  is  less  than  a 
unit. 

G.  An  impi'oper  fraction  is  one  whose  numerator 
is  equal  to,  or  greater,  than  the  denominator ;  its 
value  is  equal  to,  or  greater,  than  a  unit. 

7.  A  mixed  number  is  a  whole  number  joined  with 
a  fraction. 

8.  What  kind  of  a  fraction  is  |  ?     What  is  the  4 
called  ?     What  does  it  show  ? 

9.  In  the  fraction  -f ,  what  is  the  3  called  ?     What 
does  it  show  ? 

10.  Into  how  many  equal  parts  must  a  thing  be 
divided   to   produce   the   fraction  |  ?  how  many  of 
these  parts  must  be  taken  ? 

11.  What  kind  of  a  fraction  is  |  ?     Why  ? 

12.  What  kind  of  a  number  is  6f  ?     Why  ? 

13.  How  would  you  obtain  £  of  any  thing  ? 

14.  How  would  you  obtain  |  of  any  thing  ? 

15.  How  many  times  |  in  6  ? 

ANALYSIS.  Since  in  1  there  are  4  times  J,  or  J,  in  6 
there  are  6  times  f ,  or  2£.  Therefore  there  are  24  times  £ 
til  6. 

16.  How  many  times  J  in  4  ?  in  8  ?  in  9  ?  in  12  ? 

17.  How  many  times  £  in  3  ?  in  5  ?  in  7  ?  in  8  ? 

18.  How  many  times  j  in  2  ?  in  4  ?  in  5  ?  in  7  ? 

19.  How  many  times  ^  in  5  ?  in  6  ?  in  7  ?  in  9  ? 

20.  How  many  times  ^  in  3  ?  in  4  ?  in  6  ?  in  7  ? 

21.  How  many  times  |  in  3|  ?  in  4|  ?  in  7|  ? 

22.  How  many  times  |  in  2$  ?  in  5f  ?  in  6f  ? 

23.  How  many  times  -^  in  5^  ?  in  7TV  ?  in 


44.]  INTELLECTUAL   ARITHMETIC.  69 

24.  In  12J  how  many  thirds  ? 

25.  In  7|  how  many  fifths  ? 

26.  In  10f  how  many  eighths  ? 

27.  In  9  ^  how  many  twelfths  ? 

28.  In  15|  how  many  fourths  ? 

29.  Reduce  20 1  to  an  improper  fraction. 

30.  Reduce  8|  to  an  improper  fraction. 

31.  Reduce  7-J-J  to  an  improper  fraction. 

32.  Reduce  8|  to  an  improper  fraction. 

33.  Reduce  25f  to  an  improper  fraction. 

34.  How   do   you   reduce  a  whole  number  to  a 
fraction  having  a  required  denominator  ? 

35.  How  do  you  change  a  mixed  number  to  an 
improper  fraction  ? 


44.     1.   In  ^  how  many  times  1  ? 

ANALYSIS.  Since  |  equal  1,  ^  are  as  many  times  1 
as  |  are  contained  times  in  J?6-;  |  are  contained  in  -^  * 
times.  Therefore  lf  are  4  ta'mes  1,  or  4. 

2.  In  %£-  how  many  times  1  ? 

3.  In  42-  how  many  times  1  ? 

4.  In  -^  how  many  times  1  ? 

5.  In  -L2A  how  many  times  1  ? 

6.  In  II  how  many  times  1  ? 

7.  In  -Mp  how  many  times  1  ? 

8.  How  many  times  1  in  f |  ?  in  |«.  ?  in  f|  ? 

9.  How  many  times  1  in  -^  ?  in  4^  ?  in  ^  ? 

10.  How  many  times  1  in  -^  ?  in  -4^-?  in  \\  ? 

11.  How  many  times  1  in  \^-  ?  in  J^-  ?  in 

12.  How  many  times  1  in  -i^  ?  in  ^L  ?  in 
IS.  How  many  times  1  in  ty  ?  in  ^-^  ?  in 
14.  How  many  times  1  in  $|-  ?  in  ±^  ?  in 


70  INTELLECTUAL   ARITHMETIC.  [4*5. 


15.  How  many  times  1  in  -££  ?  in  f  f  ?  in 

16.  How  do  you  reduce  an  improper  fraction  to  a 
whole  or  mixed  number  ? 

17.  Reduce  £f  to  an  equivalent  whole  number. 

18.  Reduce  *££•  to  an  equivalent  mixed  number. 

19.  Reduce  &£  to  an  equivalent  mixed  number. 

20.  Reduce  ^  to  an  equivalent  mixed  number. 

21.  Express  tiie  value  of  *ffi  in  a  whole  number. 

22.  Express  the  value  of  f-|-g-  in  a  mixed  number. 

23.  Express  the  value  of  -^  in  a  mixed  number. 


45.     1.   In  f  of  1,  how  many  sixths  ? 

ANALYSIS.  Since  in  I  there  are  g,  in  §  of  1,  there 
are  2  times  \  of  g  ;  \  of  §  is  f ,  and  2  times  §  are  }. 
Therefore,  <£c. 

2.  In  ^  of  1  how  many  tenths  ? 

3.  In  I  of  1  how  many  twentieths  ? 

4.  In  |  of  1  how  many  fortieths  ? 

5.  In  |  of  1  how  many  tenths  ? 

6.  In  -j  of  1  how  many  sixteenths  ? 

7.  In  f  of  1   how  many  twenty-firsts  ? 

8.  In  |  of  1   how  many  thirty-sixths  ? 

9.  In  |  of  1  how  many  twelfths  ? 

10.  In  |  of  1  how  many  twenty-fifths  ? 

11.  In  -^  of  1  how  many  sixtieths  ? 

12.  In  |  of  1  how  many  eighteenths  ? 

13.  In  -Jjj-  of  1  how  many  fortieths  ? 

14.  In  2%-  of  1   how  many  eightieths  ? 

15.  ln  i|  of  1  how  many  thirtieths  ? 

16.  In  |  of  1  how  many  eighths  ? 

17.  In  I  of  1  how  many  fourteenths? 


INTELLECTUAL   ARITHMETIC.  71 

18.  In  f  of  1  how  many  twenty-sevenths  ? 

19.  In  |  of  1   how  many  fifty-sixths  ? 

20.  In  T4r  of  1  how  many  forty-fourths  ? 

21.  In  -1--J-  of  1  how  many  thirty-seconds  ? 

22.  In  ^  of  1  how  many  eightieths  ? 

23.  In  If  of  1  how  many  ninetieths  ? 

24.  In  J I  of  1  how  many  one  hundred  twentieths  ? 

25.  How  many  sixths  in  if  ? 

ANALYSIS.  Since  in  1  there  are  ||,  in  %  of  1  are  £  of 
||,  or  -j3ff  ;  and  ^  is  contained  in  ||,  5  times.  Therefore 
in  -f  |  are  5  sixths. 


26.  How  many  eighths  in  A  ? 

27.  How  many  fourths  in 

Oft        TT/S\rr   w»an\r   -flii-nrlc!   in     2 


•  i*1  T92" 
-||  ? 

in 


£l.  Jiuw  many  louiiiis  111  -g-g-  ;    i. 

28.  How  many  thirds  in  f$  ?  in 

29.  How  many  sevenths  in  J|  ?  in  t 

30.  How  many  twelfths  in  §|-  ?  in  ^ 

31.  How  many  ninths  in  |^  ?  in  |-g- 

32.  How  many  sixths  in  ||  ?  in  ^|  '4 

33.  How  many  eighths  in  |--|  ?  in  |~§-  ? 

34.  How  many  fourteenths  in  J|  ?  in  \ 

35.  How  many  fifths  in  f  £  ?  in  ||  ? 

36.  How  many  sevenths  in  ||-  ?  in  ||- 1 

37.  How  many  fourths  in  ||  ?  in  ^-f  ? 

38.  How  many  sixths  in  |~§-  ?  in  ^f  ? 

39.  How  many  halves  in  ||  ?  in  ||  ? 

40.  How  many  tenths  in  |£  ?  in  -|^-  ? 

41.  How  many  fifteenths  in  ||-  ?  in  f  f 

42.  How  many  elevenths  in  ||  ?  in  J| 

43.  How  many  sixteenths  in  |f  ?  in  -J-j] 

44.  How  many  twentieths  in  ^j-  ?  in  1 

45.  How  many  twenty-fourths  in  ||  ?  i 


72  INTELLECTUAL   ARITHMETIC.  [46. 

46.     1.   Reduce  ^  to  its  lowest  terms. 

NOTB.     A  fraction  is  snid  to  be  in  its  lowest  terms  when  no  number 
greater  than  1  will  exactly  divide  both  numerator  and  denominator. 


2. 

Reduce 

A 

to 

its 

lowest 

terms. 

3. 

Reduce 

M 

to 

its 

lowest 

terms. 

4. 

Reduce 

to 

its 

lowest 

terms. 

5. 

Reduce 

if 

to 

its 

lowest 

terms. 

6. 

Reduce 

lo 

to 

its 

lowest 

terms. 

7. 

Reduce 

H 

T2 

to 

its 

lowest 

terms. 

8. 

Reduce 

tt 

to 

its 

lowest 

terms. 

9. 

Reduce 

?! 

to 

its 

lowest 

terms. 

10. 

Reduce 

f! 

to 

its 

lowest 

terms. 

11. 

Reduce 

ft 

to 

its 

lowest 

terms. 

12. 

Reduce 

to 

its 

lowest 

terms. 

13. 

Reduce 

9$ 

to 

its 

lowest 

terms. 

14. 

Reduce 

M 

to 

its 

lowest 

terms. 

15. 

Reduce 

to 

its 

lowest 

terms. 

16. 

Reduce 

to 

its 

lowest 

terms. 

17. 

Reduce 

to 

its 

lowest 

terms. 

18. 

Reduce 

j^ 

to 

its 

lowest 

terms. 

19. 

Reduce 

M 

to 

its 

lowest 

terms. 

20. 

Reduce 

4y 

to 

its 

lowest 

terms. 

21. 

Reduce 

J^. 

to 

its 

lowest 

terms. 

22. 

Reduce 

w 

to 

its 

lowest 

terms. 

23.   How  do  you  reduce  a  fraction  to  its  lowest 
terms  ? 


HEM  ARKS.  1.  If  the  numerator  be  multiplied  by  any  number,  the 
value  of  the  fraction  will  be  multiplied  as  many  times  as  there  are  units 
in  the  multiplier. 

2.  If  the  numerator  be  divided  by  any  number,  the  value  of  the  fraction 
will  be  divided  as  many  times  as  there  are  units  in  the  divisor. 

3. .If  the  denominator  be  multiplied  by  any  number,  the  value  of  the 
fraction  will  be  divided  as  many  times*  as  there  are  units  in  the  multi- 
plier. 


47.]  INTELLECTUAL   ARITHMETIC.  73 


Fractions  are  said  to  have  a  common  denominator 
when  their  denominators  are  alike.  Any  number  that  can 
be  divided  by  each  of  the  denominators  of  the  given  frac- 
tions may  be  taken  for  the  common  denominator. 

1.  Reduce  ^  and  |-  to  fractions  having  a  common 
denominator. 

ANALYSIS.  12  is  exactly  divisible  by  4  and  3,  and  may 
therefore  be  taken  for  a  common  denominator.  Since  in  1 
there  are  \%,  in  %  of  1  there  must  be  £  of  -ff  ,  or  -fa,  and  in 
%  of  I  there  must  be  f  of  |f  ,  or  ^.  Therefore  £  and  § 
are  equal  to  -fa  and  -f^. 

2.  Reduce  J  and  |  to  fractions  having  a  common 
denominator. 

3.  Reduce  |  and  |  to  a  common  denominator. 

4.  .Reduce  J  and  |  to  a  common  denominator. 

5.  Reduce  |  and  f  to  a  common  denominator. 

6.  Reduce  f  and  ^  to  a  common  denominator. 

7.  Reduce  |  and  |  to  a  common  denominator. 

8.  Reduce  |,  ^,  and  £  to  a  common  denominator. 

9.  Reduce  f  ,  ^,  and  -^  to  a  common  denominator. 

10.  Reduce  ^,  -^   and  ^  to  a  common  denomi- 
nator. 

11.  Reduce  J,  -fg  and  £  to  a  common  denominator. 

12.  Reduce  |,  |,  |  and  |  to  a  common  denomi- 
nator. 

13.  Reduce  ^,  ^  and  ^  to  a  common  denomi- 
nator. 

14.  Reduce  1^,  2^  and  f  to  a  common  denomi- 
nator. 


4.  If  the  denominator  be  divided  by  any  number,  the  value  of  the  frac- 
tion will  be  multiplied  as  many  times  as  there  are  units  in  the  divisor. 

5.  If  both  numerator  and   denominator  be  multiplied  by  the  same 
number,  the  value  of  the  fraction  will  not  be  changed. 

6.  If  both  numerator  and  denominator  be  divided  by  the  same  number 
the  value  of  the  fraction  will  not  be  changed. 


74  INTELLECTUAL   ARITHMETIC.  [48. 

48.  1.  James  has  f  of  a  dollar,  John  |  of  a 
dollar,  and  George  |  of  a  dollar ;  how  many  fifths 
of  a  dollar  have  they  all  ?  how  many  dollars  ? 

ANALYSIS.  They  all  have  the  sum  of  J  +  I  +  t>  e(lua^ 
to  -*5°-  dollars,  equal  to  2  dollars.  Therefore,  fyc. 

2.  Jane  had  $  of  a  dollar    and  her  father  gave 
her  ^  of  a  dollar  more ;  how  much  had  she  then  ? 

3.  Austin  buys  a  pair  of  skates  for  £  of  a  dollar, 
a  pair  of  mittens  for  f  of  a  dollar,  and  a  slate  for  £ 
of  a  dollar  ;  what  is  the  cost  of  all  ? 

4.  A  grocer  sold  £  dozen  eggs  to  one  man,  £  of  a 
dozen  to  another,  and  |  of  a  dozen  to  another  ;  how 
many  dozen  did  he  sell  to  all  ? 

NOTE.     Fractions  having  different  denominators  must  be  reduced  to  a 
common  denominator  before  adding  or  subtracting. 

5.  Mary  paid  -|  of  a  dollar  for  some  ribbon,  |  of 
a  dollar  for  a  pair  of  gloves  and  £  of  a  dollar  for  a 
pair  of  hose  ;  what  was  the  cost  of  the  whole  ? 

6.  Sold   |  of  an  acre  of  land  to  one  man,  f  to 
another    and  -J?  to  another ;   how  much  was  sold 
to  all? 

7.  A  laborer  dug  £  a  rod  of  ditch  the  first  hour, 
|  of  a  rod  the  seconcf,  |  the  third  and  -^  the  fourth ; 
how  many  rods  did  he  dig  in  4  hours  ? 

8.  A  farmer  sold  ^  of  his  grain  to  one  man,  £  to 
another,  ana  ^  to  another  ;  what  part  of  his  grain 
did  he  sell  ? 

9.  Henry  paid  £  of  a  dollar  for  a  sled,  J  a  dollar 
for  a  kite  and  £  of  a  dollar  for  a  string ;  what  was 
the  cost  of  the  whole  ? 

10.  Emma  paid  2^  dollars  for  a  dress,  If  dollars 
for  a  pair  of  shoes  and  ^  of  a  dollar  for  some  ribbon ; 
what  was  the  cost  of  the  whole  ? 

NOTE.     Add  the  whole  numbers  and  the  fractions  separately,  and  then 
unite  their  sums. 


48.]  INTELLECTUAL   ARITHMETIC.  75 

11.  Milton  saved  -|  of  a  dollar  one  week,  f  of  a 
dollar  the  next,  1|-  the  next  and  2^  the  next ;  how 
much  did  he  save  in  4  weeks  ? 

12.  Albert  picked  2^  bushels  of  apples  from  one 
tree,  3f  from  another    and  8£  from  another ;  how 
many  bushels  did  he  pick  from  the  8  trees  ? 

18.  If  it  take  4  J  yards  of  cloth  for  a  coat,  2-£  yards 
for  a  pair  of  pantaloons,  and  |-  of  a  yard  for  a  vest, 
how  many  yards  of  cloth  will  it  take  for  the  whole  ? 

14.  If  a  man  walk  12 1  miles  in  the  forenoon  and 
10  i  miles  in  the  afternoon,  how  many  miles  does  he 
walk  during  the  day  ? 

15.  Harvey  bought  a  sled  for  62i  cents  and  sold 
it  for  12^  cents  more  than  he  gave  lor  it ;  how  much 
did  he  receive  for  it  ? 

16.  Three  men  bought  a  horse.     A  paid  25^ 
dollars,  B  paid  30|-  dollars  and  C  paid  35|  dollars"; 
what  was  the  cost  of  the  horse  ? 

17.  If  coal  is  worth  5A  dollars  a  ton,  and  wood 
is  worth  3T62-  dollars  a  cord,  what  will  be  the  cost  of 
one  ton  of  coal  and  two  cords  of  wood  ? 

18.  Find  the  sum  of  ^  and  -^. 

19.  Find  the  sum  of  fa  -f  and  fa 

20.  Find  the  sum  of  fa  |  and  -f$. 

21.  Find  the  sum  of  ^,  -^  and  f . 

22.  Find  the  sum  of  fa  |  and  £. 

23.  Add  together  fa  ^  and  -f-%. 

24.  Add  together  -^,  T^  and  ^. 

25.  Add  together  ^,  fa  -^  and  fa 

26.  Add  together  -^ ,  |-  and  |. 

27.  Add  together  |,  fa  -fo  and  fa 

28.  Add  together  fa  fa  fa  1  and  £ 

29.  What  is  the  sum  of  2^  and  s|  ? 

30.  What  is  the  sum  of  8|  and 


76  INTELLECTUAL   ARITHMETIC.  [49. 


31.  What  is  the  sum  of  14£,  10£  ,  and  5J  ? 

32.  What  is  the  sum  of  7-^  +  15|  +  10J  ? 

33.  What  is  the  sum  of  25-|  +  13|  +  5^  ? 

34.  What  is  the  sum  of  6$  +  7  j  +  4f  ? 

35.  What  is  the  sum  of  A  +  11£  +  14|  + 

36.  What  is  the  sum  of  3^  +  6J  +  |  + 

37.  What  is  the  sum  of  6  +  14&  +  5^  + 

38.  What  is  the  sum  of  20  +  7^T  + 


49.     1.   Amos  having  f  of  a  dollar,  gave  f  of  a 
dollar  to  a  beggar ;  how  much  had  he  left  ? 

ANALYSIS.     He  liad  left  the  difference  between  %  and  f 
of  a  dollar  ;  £  —  §  =  f  of  a  dollar.      Therefore,  $c. 

2.  Norman  had  |  of  a  bushel  of  peaches  ;  he  sold 
|  of  a  bushel ;  what  part  of  a  bushel  had  he  left  ? 

3.  Nancy  paid  |  of  a  dollar  for  a  geography  and 
|  of  a  dollar  for  a  philosophy ;  for  which  did  she  pay 
the  more,  and  how  much  ? 

4.  Two  men  own  a  piece  of  property  together; 
one  owns  ^  of  it ;  how  much  does  the  other  own  ? 

5.  When  rye  is  worth  ^  of  a  dollar  per    bushel 
and  corn  is  worth  |  of  a  dollar,  what  is  the  differ- 
ence in  the  price  ? 

6.  A  grocer  sells  ^  of  a  box  of  tea  from  a  box  £ 
full ;  what  part  of  the  whole  box  is  left  ? 

7.  Henry  can  run  £  of  a  mile  in  the  same  time 
that  John  can  run  |^  ;  which  runs  the  farther,   and 
how  much  ? 

8.  Parley  gave  £  of  a  dollar  for  a  vest  and  f  of  a 
dollar  for  a  pair  of  shoes ;  what  was  the  difference 
in  the  cost  ? 

9.  A  gentleman,  owning  a  boat,  sold  -^   of  it; 
how  much  of  it  did  he  still  own  ? 


49.]  INTELLECTUAL    ARITHMETIC.  77 

10.  If  Robert  earn  7f  dollars  a  week  and  Her- 
man earn  6^  dollars  a  week,  how  much  more  than 
Herman  does  Robert  earn  ? 

11.  Arthur  gathered  10£  quarts  of  chestnuts  and 
sold  7^  quarts ;  how  many  quarts  had  he  left  ? 

12.  From  a  piece  of  cloth  containing  12|  yard?, 
5|  yards  were  cut ;  how  many  yards  remained  ? 

13.  If  I  put  15|  dollars  in  the  bank  at  one  time, 
how  much  must  I  afterwards  put  in  to  make  the  sum 
20  dollars  ? 

14.  From  a  hogshead  of  molasses,  9  f  gallons  were 
drawn  ;  how  many  gallons  remained  ? 

15.  Edgar  will  be  14  years  old  3  ^  years  hence ; 
how  old  is  he  now  ? 

16.  From  a  jug  of  molasses  containing  1  gallon, 
•£  of  a  quart  was  used ;  how  much  was  left  ? 

17.  If  I  buy  a  book  for  f  of  a  dollar,  how  much 
change  must  be  returned  to  me  for  a  3  dollar  bill  ? 

18.  A  lady,  having  18 1  dollars,  bought  a  bonnet 
for  5f  dollars  ;  how  much  money  had  she  left  ? 

19.  What  is  the  difference  between  I-  and  f  ? 

I  O 

20.  What  is  the  difference  between  ^  and  I  ? 

21.  What  is  the  difference  between  A  and  |  ? 

o 

22.  What  is  the  difference  between  1J  and  f  ? 

23.  What  is  the  difference  between  3f  and  1|  ? 

24.  What  is  the  difference  between  16f  and  9J? 

25.  What  is  the  difference  between  20  and  12|  ? 

26.  How  many  are  |-  —  |  ? 

27.  How  many  are  4|-  —  ^  ? 

28.  How  many  are  12  —  6T9?  ? 

29.  How  many  are  36 J  —  24f  ? 

30.  How  many  are  25}  — 

31.  How  many  are  16  —  9|  ? 

32.  .How  many  are  28  —  17|  ? 


78  INTELLECTUAL    ARITHMETIC.  [5O. 

5O.     1.   Mr.  Smith  sold  £  of  his  estate  to  A,  £  of 
it  to  B  and  |  to  C ;  what  part  remained  unsold  ? 

2.  A  gambler  lost  in  play  £  and  £  of  his  money ; 
what  part  had  he  left  ? 

3.  A  lady  paid  £  of  her  money  for  a  bonnet,  J  for 
a  shawl  and  |-  for  a  pair  of  gaiters ;  what  part  had 
she  left  ? 

4.  A  laborer  worked  3  days  for  1 J,  |,  and  1|  dol- 
lars ;  had  he  received  2  dollars  a  day,  how  much 
more  would  he  have  received  ? 

5.  From  a  piece  of  calico  containing  32|  yards, 
two   dress   patterns  were   cut,  one   containing  10£ 
yards    and  the  other  12 1  yards  ;   how  many  yards 
remained  in  the  piece  ? 

6.  I  deposited  in  the  bank  at  one  time  $20^,  at 
another  $15| ;  how  much  more  must  I  deposit  to 
make  the  amount  $50  ? 

7.  Paid  $i)|  for  a  barrel  of  flour,  $5f  for  a  ton  of 
coal,  and  gave  in  payment  a  10  dollar  bill  and  a  5 
dollar  bill ;  how  much  change  must  be  returned  to 
me? 

8.  A  merchant  bought  5  barrels  of  flour,  at  $15  a 
barrel,  and  paid  $45-^-  in  goods  and  the  remainder 
in  cash  ;  how  much  cash  did  he  pay  ? 

9.  If  you  divide  $80  among  three  men,  giving  the 
first  J  of  it,  and  the  second  $35 1,  what  will  the  third 
receive  ? 

10.  A  farmer,  having  120  bushels  of  oats  to  sell, 
sold  15J  bushels  more  than  i  of  them  at  one  time, 
and  20  bushels  less  than  J  ot  them  at  another  time ; 
how  many  bushels  had  he  left  ? 

11.  Asaph  gave  ^  of  his  money  for  a  sled,  ^  for  a 
cap,  and  had  39  cents  left ;  how  much  had  he  at  first  ? 

12.  Morgan  is  lOf  years  old,  Myron  is  9|  years 
old,  and  the  sum  of  their  ages  is  5|  years  more  than 
Martin's  age  ;  how  old  is  Martin  ? 


5O.]  INTELLECTUAL  AEITHMETIC.  79 

13.  James  is  9J  years  old,  and  Lewis  is  5^  years 
less  than  twice  as  old  as  James ;  what  is  the  differ- 
ence in  their  ages  ? 

14.  A  man,  having  $64,  bought  3  cows  ;  for  the 
first  -cow  he  gave  ^  of  it,  for  the  second  |  of  it,  and 
the  remainder  for  the  third ;  what  was  the  cost  of 
the  third  cow  ? 

15.  A  grocer  drew  from  a  hogshead  20f  gallons 
of  molasses  at  one  time,  and  25|-  gallons  at  another ; 
how  many  gallons  remained  ? 

16.  What  number  must  be  taken  from  36  that  the 
remainder  may  be  7f-  ? 

17.  From  what  number  must  9i  be  taken  to  leave 
12*  ? 

18.  What  number  must  be  added  to  16^  that 
the  sum  may  be  25  J  ? 

19.  A  person  being  asked  his  age,  replied  that  if 
4|  years  were  added  to  12|  years,  the  sum  would  be 
|  his  age  ;  what  was  his  age  ? 

20.  A  person,  undertaking  a  journey  of  60  miles, 
traveled  ^  of  the  distance  the  first  day,  £  of  the 
remainder  the  second  day,  and  f  of  the  remainder 
the  third  day ;  how  far  from  his  place  of  destination 
was  he  at  the  close  of  the  third  day  ? 

21.  What  is.  the  difference  between  17|  and  5| 

+  6£? 

22.  What  is  the  difference  between  25^  and  11| 
+  7|? 

23.  What  is  the  difference  between  9  +  12|  and 
8f  +41? 

24.  From  301  take  201  +  3^. 

25.  From  40  —  lOf  take  7£  +  5J. 

26.  From  281  take  211  _  54.. 

27.  From  f  +  \  +  f  take 

28.  From  3  +  |  +  f  take 


80  INTELLECTUAL   ARITHMETIC.  [51. 

51.  1.  What  will  5  pounds  of  tea  cost  at  ^  of  a 
dollar  a  pound  ? 

ANALYSIS.  Since  1  pound  cost  J  of  a  dollar,  5  pounds, 
which  are  5  times  1  pound,  will  cost  5  times  £  ,  or  *£,  of  a 
dollar,  equal  to  $3  J.  Therefore  5  pounds  of  tea,  at  £  of  a 
dollar  a  pound,  will  cost 


2.  What  cost  4  yards  of  linen  at  f  of  a  dollar  a 
yard? 

3.  When  sugar  is  \  of  a  dollar  a  pound,  what  will 
25  pounds  cost  ? 

4.  If  I  of  a  pound  of  butter  last  a  family  1  day, 
how  many  pounds  will  last  them  one  week  ? 

5.  What  will  be  the  cost  of  10  peaches  at  J  of  a 
cent  apiece  ? 

6.  If  a  man  earn  ^  of  a  dollar  a  day,  how  much 
will  he  earn  in  12  days  ? 

7.  If  1  peck  of  pears  cost  £  of  a  dollar,  what  will 
2  bushels  cost  ? 

8.  How  many  loaves  of  bread  must  you  give  to  8 
beggars,  if  you  give  them  |  of  a  loaf  apiece  ? 

9.  At  I  of  a  dime  a  pound,  what  will  15  pounds 
of  nails  cost  ? 

10.  What  will  9  yards  of  silk  cost  at  f£  of  a  dollar 
a  yard  ? 

11.  George  had  £$•  of  a  dollar,  and  William  had  8 
times  as  much  ;  how  much  had  William  ? 

12.  If  1  horse  eat  ^  of  a  ton  of  hay  in  a  month, 
how  much  will  10  horses  eat  ? 

13.  How  many  are  9  times  |  ?  12  times  |  ?  14 
times  ^  ?  20  times  -fa  ? 

14.  If  1  man  can  reap  ^  of  an  acre  of  rye  in  a 
day,  how  much  can  11  men  reap  ? 

15.  How  many  barrels  of  flour  will  be  given  to  9 
poor  families,  if  each  receive  ^  of  a  barrel  ? 

16.  How  many  are  12  times  ^  ?  16  times  |  ? 


09.]  INTELLECTUAL   ARITHMETIC.  81 

17.  Bought  6  bushels  of  corn  at  $|  a  bushel,  and 
had  $4  left ;  how  much  money  had  I  at  first  ? 

18.  If  1  quart  of  molasses  cost  $^3g,  what  will  4 
gallons  cost  at  the  same  rate  ? 

19.  If  a  boy  give  each  of  his  4  companions  f  of  a 
quart  of  chestnuts,  and  have  4|-  quarts  left,  how 
many  quarts  had  he  at  first  ? 

20.  How  do  you  multiply  a  fraction  by  a  whole 
number  ? 


1.    If  1  box  of  raisins  cost  $2f ,  what  will  5 
boxes  co^t  ? 

ANALYSIS.  If  1  box  of  raisins  cost  $2 j,  5  boxes,  which 
are  5  times  1  box,  will  cost  5  times  $2£ ;  5  times  f  are  J^-, 
or  $3£;  5  ft'wes  $2  are  $10;  $3f  added  to  $10  are 
$13|.  Therefore,  if  1  fo#  #/*  raisins  cost  $2f,  5  fo#es 
will  cost  $13f. 

2.  At  12 J  cents  a  pound,  what  will  9  pounds  of 
butter  cost  f 

3.  At  $6f  a  barrel,  what  will  7  barrels  of  flour 
cost? 

4.  How  many  bushels  of  grain  will  15  bags  hold, 
if  they  hold  2-J-  bushels  apiece  ? 

5.  What  will  be  the  cost  of  12  pounds  of  rice,  afc 
6^  cents  a  pound  ? 

6.  What  will  9  dozen  of  eggs  cost  at  11 J  cents  a 
dozen  ? 

7.  What  will  7  yards  of  cloth  cost  at  $5 A  a  yard  ? 

8.  If  1  barrel  of  fish  cost  $14f ,  what  will  6  barrels 
cost  ? 

9.  If  1  horse  eat  3^  tons  of  hay  in  5  months,  how 
many  tons  will  20  horses  eat  in  the  same  time  ? 

10.  If  1  pint  of  wine  cost  $1|,  what  will  1  gallon 
cost  ? 

6 


82  INTELLECTUAL   ARITHMETIC.  [«53. 

11.  If  5  men  can  do  a  piece  of  work  in  lOf  days> 
how  long  will  it  take  1  man  to  do  the  same  ?   * 

12.  If  a  grain  of  gold  is  worth  4*  cents,  what  is  1 
pennyweight  worth  V 

13.  A  grocer  sold  9  pounds  of  coffee  at  12£  cents 
a  pound,  and  7  pounds  of  sugar  at  8|  cents  a  pound ; 
1  ow  much  did  he  receive  for  both  ? 

14.  If  it  take  34  yards  of  cloth  for  a  coat,  and  24 
yards  for  a  pair  of  pantaloons,  how  many  yards  will 
be  required  to  make  3  of  each  ? 


53.  1.  If  1  pound  of  cheese  cost  10  cents,  what 
will  5|-  pounds  cost  ? 

ANALYSIS.  Since  1  pound  cost  10  cents,  5g  pounds, 
which  are  5§  times  1  pound,  will  cost  5§  times  10  cents  ; 
5  times  10  cents  are  50  cents,  f  of  10  cents  are  3  tines  %  of 
10  cents  ;  £  of  10  cents  is  If  cents,  and  g  of  10  cents  are  3 
times  1%  cents,  or  3§  cents,  which  added  to  50  cents  make 
53  J  cents.  Therefore,  fyc. 

2.  If  a  horse  travel  6  miles  an  hour,  how  far  will 
he  travel  in  7|  hours  ? 

3.  If  a  person's  expenses  be  $12  a  week,  what 
will  they  be  for  9|  weeks  ? 

4.  What  will  4|  barrels  of  cider  cost  at  $3  a  barrel  ? 

5.  What  will  lOf  pounds  of  honey  cost  at  12  cents 
a  pound  ? 

6.  What  will  15f  bushels  of  potatoes  cost  at  6 
shillings  a  bushel  ? 

7.  If  a  pint  of  wine  is  worth  40  cents,  what  are  3f 
pints  worth  ? 

8.  If  a  man  can  build  4  rods  of  wall  in  a  day,  how 
many  rods  can  he  build  in  7|  days  ? 

9.  If  a  barrel  of  flour  last  a  family  6  weeks,  how 
long  will  4-J  barrels  last  them  ? 


INTELLECTUAL   ARITHMETIC.  83 

10.  If  stage  fare  is  4  cents  a  mile,  what  will  it 
cost  to  ride  20f  miles. 

11.  If  a  merchant  pay  12  shillings  for  3  caps,  and 
sell  them  for  6|  shillings  apiece,  what  is  his  gain  ? 

12.  Bought   9£   yards  of  silk  at  12   shillings  a 
yard,  and  12f  pounds  of  tea  at  7  shillings  a  pound  ; 
how  much  more  did  the  silk  cost  than  the  tea  ? 

13.  If  I  buy  8|  tons  of  coal,  at  $5  a  ton,  how 
much  less  than  $50  will  it  cost  ? 

14.  A  woman   took  6|   dozen   eggs   to  market, 
which  she  sold  for  12  cents  a  dozen  ;  she  received  in 
payment  4|  yards  of  calico  at  10  cents  a  yard,  3^ 
yards  of  ribbon  at  8  cents  a  yard ;  how  much  was 
still  her  due  ? 

15.  If  |  of  a  barrel  of  flour  last  a  family  1  month, 
how  many  barrels  will  last  8  such  families  6|  months  ? 

16.  What  is  the  product  of  4^  times  9  multiplied 
by  3? 

17.  What  is   the  product  of  5  times  3|  multi- 
plied by  2  £  ? 

18.  Multiply  4|-  times  10  by  |  of  15. 

19.  Multiply  3|  times  6  by  |  of  24. 

20.  Multiply  4-f  by  f  of  16. 

21.  Multiply  2  times  9£  by  2^  times  4. 

22.  Multiply  5  times  3£  by  -f  of  15. 

23.  What   is   the  sum   of  8   times   7T%   and   4| 
times  12  ? 

24.  What  is   the   sum   of  6|   times   11   and   12 
times  5f  ? 

25.  What  is  the  difference  between  4f  times  10 
and  3  times  9|  ? 

26.  What  is  the  difference  between  7  times  8J  and 
101  times  5  ? 

27.  How  many  are  12|  times  7  ?  9f  times  10  ? 

28.  How  many  are  5f  times  15  ?  3^  times  40  ? 


84  INTELLECTUAL   ARITHMETIC. 

54.  1.  A  man,  owning  £  of  a  store,  sold  4  of 
his  share ;  what  part  of  the  whole  store  dia  he 
sell? 

ANALYSIS.  He  sold  \  of  \  of  the  store.  Since  $  is 
equal  to  J,  |  of  \  is  equal  to  \  of  |,  or  £.  Therefore, 
he  sold  ^  of  the  store. 

2.  James  had  |  of  a  dollar,  and  gave  -J-  of  it  to  a 
beggar ;  what  part  of  a  dollar  did  he  give  away  ? 

3.  A  boy,  having  J  of  a  watermelon,  gave  away  * 
of  what  he  had  ;  what  part  of  the  whole  melon  did 
he  give  away  ? 

4.  If  a  yard  of  crape  cost  |  of  a  dollar,  what  will 
J  of  a  yard  cost  ? 

5.  If  I  own  £  of  an  acre  of  land,  and  sell  £  of  it, 
what  part  of  an  acre  do  1  sell  ? 

6.  If  a  bushel  of  apples  be  worth  %  of  a  dollar, 
what  is  J  of  a  bushel  worth  ? 

7.  John  is  £  as  old  as  his  father,  and  Henry  is  £ 
as  old  as  John  ?  what  part  of  his  father's  age  is 
Henry's  age  ? 

8.  A  merchant,  having  |  of  a  hogshead  of  molas- 
ses, sold  £  of  what  he  had  ;  what  part  of  the  whole 
hogshead  did  he  sell,  and  what  part  had  he  left  ? 

9.  Homer  bought  £  a  box  of  figs,  and  Robert  \ 
as  many  ;  what  part  of  a  box  did  both  buy  ? 

10.  C  owned  1  of  a  steamboat,  and  sold  |  of  his 
snare  ;  what  part  of  the  whole  did'he  sell  ? 

11.  Mr.   Jones,  owning  £  of  a  cotton  mill,  sold  J 
of  his  share  to  B,  and  B  sold  l  of  his  share  to  C ; 
what  part  of  the  whole  did  each  have  after  the  di- 
vision ? 

12.  A  cistern,  being  full  of  water,  sprang  a  leak, 
and  before  it  could  be  stopped  J  of  the  water  ran 
out,  but  ^  as  much  ran  in  at  the  same  time ;  what 
part  of  the  cistern  was  emptied  ? 

13.  A  poor  man,  having  1  of  a  barrel  of  flour. 


54.]  INTELLECTUAL   ARITHMETIC.  85 

gave  I  of-  it  to  a  poor  neighbor,  who  gave  ^  of  hi? 
share  to  a  poor  woman  ;  what  part  of  a  barrel  had 
each  then  ? 

14.  Andrew,  having  $|,  gave  |  of  it  for  a  knife  ; 
what  part  of  a  dollar  did  he  pay  for  his  knife  ? 

ANALYSIS.  He  paid  f  of  £  of  a  dollar.  3  fifths  of  £ 
are  3  times  1  fifth  of  £ .  £  of  £  &  ^,  cmd  f  o/  £  are  3  times 
&»  or  ^.  Therefore,  $c. 

15.  If  a  yard  of  cloth  is  worth  $|,  what  fs  \  of  a 
yard  worth  ? 

16.  Harriet,  having  |-  of  a  yard  of  silk,  gave  f  of 
it  to  her  sister ;  what  part  of  a  yard  did  she  give 
away,  and  what  part  of  a  yard  had  she  left  ? 

17.  A  man,  owning  |  of  a  farm,  sold  |  of  his  share 
to  his  brother  ;  what  part  of  the  farm  did  each  own  ? 

18.  Hannah  picked  -f$  of  a  pailful  of  strawberries, 
and  on  her  way  home  spilled  |  of  them ;  what  part 
of  a  pailful  had  she  left  ? 

19.  What  will  be   the   cost  of  f  of  a  bushel  of 
beans  at  $f  a  bushel  ? 

20.  Jacob,  having  -|  of  a  pound  of  candy,  gave  \ 
of  it  to  Mary,  and  \  of  it  to  Jane ;  what  part  of  a 
pound  had  he  left  ? 

21.  A  keeper  of  a  saloon  bought  a  cask  of  ale ;  \ 
of  it  leaked  out,  f  of  the   remainder  he  sold,  and 
what  was  left  he  kept  for  his  own  use  ;  what  part  of 
the  cask  did  he  keep  ? 

22.  How  do  you  multiply  one  fraction  by  another  ? 

23.  What  is  i  of  1?  29.    What  is  \  of  \  ? 

24.  What  is  |-  of  \  ?  30.    What  is  \  of  \  ? 

25.  What  is  ^  of  I  ?  31.   What  is  l  of  1  ? 

26.  What  are  4  of  \  ?  32.    What  is  J  of  f  ? 
2T.    What  are  f  of  f  ?           33.    What  are  J-  of  f  ? 
28.    What  are  A  of  -£-  ?         34. 


86  INTELLECTUAL   ARITHMETIC.  [55. 

55.  1.  At  $8|  a  barrel,  what  will  |  of  a  barrel 
of  flour  cost  ? 

ANALYSIS.  Since  1  barrel  cost  $8|,  |  of  a  barrel,  which 
is  3  times  £ ,  will  cost  3  times  £  of  $8|.  £  of  $8  ?'s  (2,  and 
i  o/$|  2*5  $£,  which  added  to  $2  w/r/to  §2-J.  3  ft'ww  $2 
are  $6,  and  3  times  -J  are  £,  wfo'c^  aeWeo1  to  $G  make  $6g. 
Therefore,  fyc. 

Or,  $8£  are  e^*aZ  to  \4-,  awe?  %of*£  =  ^,  or  $6f. 

2.  At  $6£  a  bushel,  what  will  f  of  a  bushel  of 
clover  seed  cost  ? 

3.  At  $12f  a  ton,  what  will  g-  of  a  ton  of  hay  cost  ? 

4.  If  a  man  travel  24}  miles  in  1  day,  how  far 
will  he  travel  in  £  of  a  "day  ? 

5.  What  will  |  of  a  barrel  of  beef  cost,  at  $15 1  a 
barrel  ? 

6.  What  will  be  the  cost  of  \  of  a  cord  of  wood, 
if  1  cord  cost  $5-t  ? 

7.  At  lOi  shillings  a  day,  how  much  can  a  man 
earn  in  |  of  a  day  ? 

8.  If  a  man  can  cut  3i  acres  of  rye  in  1  day,  how 
much  can  he  cut  in  |  of  a  day  ? 

9.  If  I  pay  $6 1  for  ajar  of  butter,  what  is  £  of  it 
worth  ? 

10.  Bought  a  horse  for  $75J,  and  sold  him  for  | 
of  what  he  cost ;  what  was  the  loss  ? 

11.  What  is  |  of  14£?  of  20|  ?  of  13|?  of  181? 

12.  What  are  f  of  9|  ?  of  12$  ?  of  16*  ?  of  214  ? 

13.  What  are  |  of  21f  ?  |  of  32J  ?  f  of  23 J  ? 

14.  At  $|  a  yard,  what  will  6£  yards  of  flannel 
cost  ? 

ANALYSIS.  Since  1  yard  costs  $§,  6£  yards  will  cost  G£ 
times  $|.  6  times  $f  are  -^  or  $4,  arco7  %  of  %  is  -£%,  or 
$£,  which  added  to  $4  makes  $4 £.  Therefore,  $c. 

Or,  6£  are  ^wa/  to  ^,  awe?  ^-  o/  f  are  ^J,  or  $4J. 
Therefore,  $c. 

15.  At  $|  a  bushel,  what  will  8|-  bushels  of  peaches 
cost? 


INTELLECTUAL   ARITHMETIC.  87 

16.  If  a  man  hoe  £  of  an  acre  of  corn  in  1  day, 
how  many  acres  can  he  hoe  in  5|  days  ? 

17.  If  a  vessel  sail  12-|  miles  in  1  hour,  how  far 
does  she  sail  in  |  of  an  hour  ? 

18.  If  a  man  has  22J-  bushels  of  clover  seed,  and 
he  sell  I  of  it,  how  much  has  he  left  ? 

19.  What  will  J  of  £  of  12  gallons  of  oil  cost,  at 
a  gallon  ? 

20.  At  $|  a  rod,  what  will  it  cost  to  dig  |-  of  f  of 
28  rods  of  ditch  ? 

21.  What  will  4*  yards  of  cloth  cost  at  $2|  a 
yard  ? 

NOTE.     Reduce  the  mixed  numbers  to  improper  fractions,  and  then 
proceed  as  in  multiplying  one  fraction  by  another. 

22.  If  you  earn  8|-  shillings  in  1  day,  how  much 
can  you  earn  in  2|  days  ? 

23.  What  cost  2|  dozen  of  eggs  at  10|-  cents  a 
dozen  ? 

24.  What  will  3f  yards  of  shalloon  cost  at  $1^ 
a  yard  ? 

25.  If  a  man  can  do  a  job  of  work  in  5|  days,  in 
what  time  can  he  do  a  job  If  times  as  large  ? 

26.  Clorinda  is  7|  years  old,  and  Augusta  is  £  as 
old  ;  how  old  is  she  V 

27.  A  man  paid  $16f  for  a  cow,  and  2J  times  as 
much  for  a  colt ;  how  much  did  he  pay  for" both? 

28.  What  is  the  product  of  3|  times  9-|  ? 

29.  What  is  the  product  of  81  times  10|  ? 

30.  What  is  the  product  of  %  of  f  of  16  multi- 
plied by  5f  ? 

31.  What  is  the  value  of  f  of  |  of  6f  ? 

32.  What  is  the  value  of  |  of  |-  of  30  ? 

33.  What  is  the  value  of  f  of  |  of  |  ? 

34.  What  is  9T^  times  f  ?  41  times  -£  ? 

35.  What  is  10^  times  2|  ?  2^  times  25J  ? 


88  INTELLECTUAL   ARITHMETIC.  [456. 


1.   If  3  pounds  of  raisins  cost  f  f-,  what  will 
1  pound  cost  ? 

ANALYSIS.  If  3  pounds  cost  $f  ,  1  pound,  which  is  $ 
of  3  pounds,  will  cost  £  of  $£,  or  $f  .  Therefore,  fyc. 

2.   If  4  slates  cost  $|,  what  will  1  slate  cost  ? 
8.   If  5  pounds  of  sugar  cost  $-|,  what  will  1  pound 
ost? 

4.  If  3  oranges  are  worth  |  of  a  melon,  what  part 
of  the  melon  is  1  orange  worth  ? 

NOTE.  It  will  be  remembered  that  a  fraction  may  be  divided  by  a 
whole  number  either  by  dividing  the  numerator  or  multiplying  the  denom- 
inator by  it.  (See  pages  72  and  73,  notes.) 

5.  If  6  pounds  of  coffee  cost  $|,  what  will  1  pound 
cost  ? 

6.  If  4  apples  cost  |-  of  a  shilling,  what  will  1 
apple  cost  ? 

7.  If  5  yards  of  sheeting  cost  f  f  ,  what  will  1  yard 
cost? 

8.  If  4  figs  cost  |  of  a  dime,  what  will  1  fig  cost  ? 

9.  What  will  1  yard  of  linen   cost,  if  4  yards 
cost  $|  ? 

10.  Marcus  had  f  of  a  melon,  which  he  wished  to 
divide  equally  between  his  2  sisters  ;  what  part  must 
he  give  to  each  ? 

11.  Oliver,  having  12  quarts  of  blueberries,  sold  | 
of  them  for  $  |-  ;  what  was  that  a  quart  ? 

12.  If  6  persons  agree  to  share  equally  |  of  a 
bushel  of  grapes,  what  part  of  a  bushel  will  each 
have  ? 

13.  If  you  divide  f  of  a  barrel  of  flour  among  3 
poor  families,  what  part  of  a  barrel  will  you  give  to 
each  ? 

14.  How  many  times  is  7  contained  in  f  ?  5  in 
if?  8inf  ?  lOin-^? 

15.  What  is  the  quotient  of  ||  divided  by  5  ?  by  7  ? 

16.  What  is  the  quotient  of  f  divided  by  3  ?  by  4  ? 


57.]  INTELLECTUAL  ARITHMETIC.  89 

57.  1.  At  $|  a  yard,  how  many  yards  of  silk 
can  be  bought  for  $6  ? 

ANALYSIS.  As  many  yards  as  $£,  the  price  of  1  yard, 
is  contained  times  in  $6  ;  $6  is  equal  to  $-2/,  and  $|  is  con- 
tained in  $-2/  8  times.  Therefore,  at  $J  a  yard,  8  yards  of 
silk  can  be  bought  for  $6» 

2.  If  a  boy  can  earn  $f  a  day,  how  long  will  it 
/take  him  to  earn  $5  ? 

3.  How  long  will  it  take  a  man  to  spend  $10  for 
cigars,  if  he  spend  $  J-  a  day  ? 

4.  When  potatoes  are  $f  per  bushel,  how  many 
bushels  can  be  bought  for  $8  ? 

5.  At  $|  a  pair,  how  many  pairs  of  shoes  can  be 
bought  for  $7  ? 

6.  How  much  butter  can  be  bought  for  $3,  at  f  j- 
a  pound  ? 

7.  How  many  times  is  4  contained  in  4  ?  in  7  ? 
in  8? 

8.  If  the  cars  run  f  of  a  mile  a  minute,  how  long 
will  they  be  in  running  25  miles  ? 

9.  If  a  horse  eat  |  of  a  bushel  of  oats  a  day,  how 
long  will  9  bushels  last  him  ? 

10.  If  a  man  walk  |-  of  a  mile  in  J  of  an  hour, 
how  long  will  it  take  him  to  walk  12  miles  ? 

11.  How  many  bushels  of  oats,  worth  $|  a  bushel, 
will  pay  for  -|  of  a  barrel  of  flour,  worth  $9  a  barrel  ? 

12.  A  farmer  sold  a  grocer  1  ton  of  hay  for  $12, 
and  received  -|-  the  amount  in  sugar  at  $|  a  pound, 
-J  in  money,  and  the  remainder  in  molasses  at  $f  a 
gallon ;  how  many  pounds  of  sugar,  and  how  many 
gallons  of  molasses,  did  he  receive  ? 

13.  If  |  of  a  barrel  of  trout  cost  $12,  what  will  1 
barrel  cost  ? 

14.  If  |  of  a  ton  of  hay  cost  $7,  what  will  1  ton 
cost  ? 


90  INTELLECTUAL   ARITHMETIC.  [58. 

15.  When  potatoes  are  worth  $*-  a  bushel,  and 
corn  $|  a  bushel,  how  many  bushels  of  potatoes  are 
equal  in  value  to  16  bushels  of  corn  ? 

16.  How  many  yards  of  ribbon,  at  $  of  a  shilling 
a  yard,  can  be  bought  for  7  shillings  ? 

17.  If  1  man  consume  £  of  a  pound  of  meat  in  a 
day,  how  many  men  would  6  pounds  supply  ? 

18.  If  f  of  a  hogshead  of  molasses  cost  $36,  what 
will  one  hogshead  cost  ? 

19.  If  |  of  an  acre  of  land  sell  for  $21,  what  will 
an  acre  sell  for  at  the  same  rate  ? 

20.  How  many  pounds  of  tea,  worth  $^  a  pound, 
must  be  given  for  9  bushels  of  apples,  worth  $J  a 
bushel  ? 

21.  How  many  times  is  |  contained  in  5  ?  in  7  ? 
in  9  ?  in  11  ?  in  15  ? 

22.  How  many  times  is  |  contained  in  12  ?  in  18  ? 
in  20  ?  in  15  ? 

23.  How  many  times  is  £  contained  in  |  ?  in  |-|  ? 
in  ft?  in  I? 

24.  How  many  times  is  %  contained  in  £  of  16  ? 
in  |  of  27  ? 

25.  How  is  a  whole  number  divided  by  a  fraction  ? 


58.     1.   At  $2  a  bushel,  how  many  bushels  of 
wheat  can  be  bought  for 


ANALYSIS.  As  many  bushels  as  $2,  the  price  of  I  bushel, 
is  contained  times  in  $11£.  11£  are  equal  to  A£,  and  2  is 
contained  in  Aj*>  -1/-,  or  5§  times.  Tfierefore,  fyc. 

Or,  2  is  contained  in  11  J,  5  times,  and  1^  or  ^over  ;  and 
2  is  contained  in  |,  f  times,  which  added  to  5  makes  5| 
times.  Therefore,  fyc. 

2.  If  6  pounds  of  coffee  cost  $lf  ,  what  is  the  cost 
of  1  pound  ? 


59.]  INTELLECTUAL   ARITHMETIC.  91 

3.  If  a  man  walk  18 1  miles  in  4  hours,  how  many 
miles  does  he  walk  in  1  hour  ? 

4.  How  many  times  will  16|  gallons  of  cider  fill  a 
vessel  that  holds  3  gallons  ? 

5.  How  many  oranges,  at  3  cents  ap.°,ce,  caij.  be 
bought  for  I  of  £  of  60  cents  ? 

6.  At  $4  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $21f  ? 

7.  If  a  turkey  cost  7  shillings,  how  many  turkeys 
can  be  bought  for  38^-  shillings  ? 

8.  At  5  shillings  a  gallon,  how  many  gallons  of 
molasses  can  be  bought  for  24|-  shillings  ? 

9.  If  a  day  laborer  earn  $8f  in  10  days,  how  much 
does  he  earn  in  1  day  ? 

10.  If  a  locomotive  run  4|  miles  in  6  minutes, 
how  far  does  she  run  in  1  minute  ? 

11.  If  12  bushels  of  oats  cost  $4|,  what  part  of  a 
dollar  will  1  bushel  cost  ? 

12.  If  7  pounds  of  coffee  cost  8|   dimes,   What 
will  1  pound  cost  ? 

13.  Divide  8|  by  5  ;  lOf  by  7  ;  15J  by  15. 

14.  Divide   9f   by    7;    18|-  by   12;    20£    by  ! 
of  16. 

15.  Divide  f  of  21  by  f  of  10.     f  of  29  by  £ 
of  63. 


59.  1.  At  $f  a  pound,  how  many  pounds  of 
tea  can  be  bought  for  $  f  ? 

ANALYSIS.  As  many  pounds  as  $§,  the  price  of  1 
pound,  is  contained  times  in  $£.  f  equal  •£$<  f  e<?wa/  ££, 
and  8  twentieths  are  contained  in  15  twentieths  1|  times. 
Therefore,  at  $|  a  pound,  Impounds  can  be  bought  for  $£. 

Or  thus  :  •£  ?s  contained  in  1,5  ft'mis,  «wc?  m  }  q/'  1  iV  i* 
contained  f  o/  5  ^'712^5,  or  -^  ^'TTZ^  ;  f  z's  contained  in  |,  ^ 
f  times,  and  ^  of  ^f-  is  *£-,  or  1 J. 


92  INTELLECTUAL   ARITHMETIC.  [«59. 

2.  How  many  pounds  of  honey,  at  1}  a  pound, 
can  be  bought  for  $  J-  ? 

3.  In   §  of  an  acre  of  land,  how  many  building 
lots  of  -^0-  of  an  acre  each  ? 

4.  If  a  horse  eat  f  of  a  bushel  of  oats  in  a  day 
in  how  many  days  will  he  eat  -£$  of  a  bushel  ? 

5.  At  |  of  a  cent  apiece,  how  many  slate  pencils 
can  be  bought  for  f  of  a  cent  ? 

6.  If  a  piece  of  ribbon  |  of  a  yard  long  be  cut 
into  pieces  £  of  a  yard  in  length,  how  many  pieces 
will  there  be  ? 

7.  A  man,  owning  |  of  a  coal  mine,  divided  his 
share  equally  among  his  sons,  giving  them  -^  each  ; 
how  many  sons  had  he  ? 

8.  Among  how  many  children  can  you  divide  -|  of 
If  melons,  if  you  give  -£  of  £  of  a  melon  to  each  '( 

9.  At  $J  a  yard,  how  many  yards  of  silk  can  be 
bought  for  $f  ? 

10.  At  |  of  -J-  of  a  dollar  a  yard,  how  many  yards 
of  ribbon  can  be  bought  for  $  ^  ? 

11.  At  $jV  a  pint,  how  much  wine  can  be  bought 


12.  When  peaches  are  worth  $|  a  bushel,  how 
many  can  be  bought  for  $|  ? 

13.  If  |  of  a  yard  of  silk  cost  $f  ,  what  will  1  yard 
cost? 

ANALYSIS.  It  will  cost  3  times  ±  of  $£,  or  £  of  $|.  £ 
of  |  is  f  ,  and  3  times  |  are  f  ,  or  $  1  £.  fJ7ierefore,  if  %  of 
a  yard  of  silk  cost  $J,  1  yard  will  cost  $1|. 

14.  What  will  1  dozen  eggs  cost,  if  |  of  a  dozen 
cost  f  of  a  dime  ? 

15.  If  f  of  a  bushel  of  corn  are  worth  -V0-  of  a 
bushel  of  rye,  how  many  bushels  of  corn  is  1  bushel 
of  rye  worth  ? 

16.  Horace  had  $f  ,  which  was  f  of  what  he  paid 
for  a  cap  ;  what  was  the  cost  of  his  cap  ? 


INTELLECTUAL   ARITHMETIC.  93 


17.  If  f  of  a  yard  of  cloth  cost  $^,  what  will  1 
yard  cost  ? 

18  James  bought  -f  of  a  pineapple,  which  was  f 
of  what  Luther  bought  ;  what  part  of  a  pineapple 
did  Luther  buy  ? 

19.  If  |  of  a  drum  of  figs  cost  $|,  what  will  1 
drum  cost  ? 

20.  How  many  times  can  a  bottle  holding  %  of  f 
of  a  gallon  be  filled  from  a  demijohn  containing  f  of 
If  gallons  ? 

21.  Divide  |  by  f;  ^  by  |, 

22.  Divide  J-f  by  f  ;  T9T  by  f  . 

23.  Dividef  by  £;  f  by  f  . 

24.  Divide  J  of  |  by  |  ;  f  of  f  by  |  of  f  . 

25.  Divide  f|  by  £  of  f  ;  29o  by  f 

26.  Divide  f|  by  ^;  ^  b7  iV 

27.  How  many  times  are  f-  contained  in  - 

28.  How  many  times  are  |  contained  in 

29.  How  many  times  are  f  contained  in  -|  ? 

30.  How  many  times  are  f  contained  in  -i|-  ? 

31.  How  many  times  are  |-  contained  in  |  ? 

32.  How  many  times  are  f  of  f  contained  in 

33.  How  many  times  are  -|  contained  in  f  of  1|  ? 
84.    How  many  times  are  |  of  f  contained  in  £  of  f  ? 
35.    |^  are  f  of  what  number  ? 


ANALYSTS.     ^  are  |  o/*4  fo*/??es  -i  q/"  |  ;  -j  •  of  ^  are  2 
4  times  ^  are  if.     Therefore^  |  ar^  |  o/  ^|. 

36.  f  are  f  of  what  number  ? 

37.  f  are  f  of  what  number  ? 

38.  -^  are  -|  of  what  number  ? 

39.  |  are  f  of  what  number  ? 

40.  are     of  what  number  ? 


94  INTELLECTUAL   ARITHMETIC.  [6O. 

CO.     1.    At  !-{?-  dollars  a  yard,  how  many  yards  of 
cloth  can  be  bought  for  $11  ? 


ANALYSIS.  As  many  yards  as  $1£,  the  price  of  1  yard, 
is  contained  times  in  $11.  $1£  are  $y;  $11  are  $$£-, 
and  -y  is  contained  in  ^£,  G  times.  Therefore,  at  $1|  a 
yard,  G  yards  of  cloth  can  be  bought  for  §11. 

2.  If  a  turkey  cost  $1£  ,  how  many  can  be  bought 
for  $9  ? 

3.  A  grocer  paid  $4f  for  some  onions,  at  the  rate 
of  $f  a  bushel  ;  how  many  did  he  buy  ? 

4.  How  many  times  will  4-f  gallons  of  campheno 
fill  a  vessel  that  holds  £  of  £  of  1  gallon  ? 

5.  If  4|  yards  of  velvet  ribbon  cost  $|,  what  will 
1  yard  cost  ? 

6.  If  3^  dozen  of  eggs  cost  $^,  what  is  the  cost 
of  1  dozen  ? 

7.  How  many  yards  of  flannel  worth  $f  a  yard 
can  be  bought  for  6  turkeys  worth  $>f  apiece  ? 

8.  If  1  man  can  do  a  piece  of  work  in  6|  days,  in 
what  time  can  4  men  do  the  same  ? 

9.  If  a  man  chop  l£  cords  of  wood  in  a  day,  how 
long  will  it  take  him  to  chop  10J  cords  ? 

NOTE.     Reduce  the  mixed  numbers  to  improper  fractions,  and  then 
divide  the  same  as  you  divide  one  traction  by  another. 

10.  If  41  baskets  of  peaches  are  worth  $3f  ,  what 
is  1  basket  worth  ? 

11.  If  51  bushels  of  apples  cost  $1*,  what  is  the 
cost  of  1  bushel  ? 

12.  If  a  man  spend  $lf  a  month  for  tobacco,  in 
what  time  will  he  spend  $101  for  the  same  purpose  ? 

13.  At  4^  shillings  a  gallon,  how  many  gallons  of 
molasses  can  be  bought  for  9|  shillings  ? 

14.  If  a  stage  run  24|  miles  in  3^  hours,  how  far 
does  it  run  in  1  hour  ? 

15.  Mr.  B.  distributed  16^  bushels  of  corn  equally 


6O.]  INTELLECTUAL   ARITHMETIC.  95 

among  some  poor  persons,  giving  them  1-J-  bushels 
each  ;  among  how  many  persons  did  he  divide  it  ? 

16.  Bought  1  of  7-J  cords  of  wood  for  *  of  $32  ; 
what  did  1  cord  cost  ? 

17.  A  father  divided  11 3 1  acres  of  land  among  his  3 
sons ;  to  the  first  he  gave  f  of  it,  and  the  remainder  he 
divided  equally  between  the  other  2 ;  how  many  acrea 

f\ir\    oar»Vi    vonoivo  ? 


cuviueu  equally 

did  each  receive  ? 


id  each  receive  ? 

18.  Divide  9J  by  6  ;  10J  by  7  ;  12|  by  31. 

19.  Divide  10J-  by  f ;  14£  by  f  ;  20|  by  |. 

20.  Divide  7J  by  3| ;  15£  by  2|  ;  8|  by  5f 

21.  Divide  16J  by  3J  ;  20 J-  by  1^  ;  11$  by  4| 
22..  Divide  |  of  $  of  14  by  f  of  3-J-. 

23.  -£  are  how  many  times      6  ? 

24.  T8_  are  now  many  times      4  ? 

25.  -|{r  are  how  many  times    15  ? 

26.  J^  are  how  many  times    6^  ? 

27.  12  are  how  many  times      f  ? 

28.  16  are  how  many  times      |  ? 

29.  25  are  how  many  times      |  ? 

30.  14  are  how  many  times    -^  ? 

31.  14f  are  how  many  times      |  ? 

32.  6|  are  how  many  times      |-  ? 

33.  21^  are  how  many  times      5  ? 

34.  32|  are  how  many  times      7  ? 

35.  17|  are  how  many  times      8  ? 

36.  15  are  how  many  times    7J  ? 

37.  18^  are  how  many  times    2J  ? 

38.  22|-  are  how  many  times    3f  ? 

39.  4T97  are  how  many  times    6|  ? 

40.  7f  are  how  many  times    4J  ? 

41.  8|  are  how  many  times    3|  ? 


96  INTELLECTUAL   ARITHMETIC.  [61. 

61.     1.   What  is  £  of  3  ? 

ANALYSIS.  That  number  which,  taken  4  times,  will 
make  3.  Since  1  fourth  of  1  is  ^  1  fourth  of  3  is  3 
times  |  of  1,  w  |  o/  1.  Therefore  \  of  3  £s  f  0/ 1,  or  f; 

2.  What  is  i  of  3  ?  of  4  ?  of    6  ?  of    7  ? 

3.  What  is  -J-  of  7  ?  of  3  ?  of    9  ?  of  15  ? 

4.  What  is  £  of  2  ?  of  4  ?  of    5  ?  of  11  ? 

5.  What  is  \  of  3  ?  of  5  ?  of    7  ?  of  13  ? 

6.  What  is  i  of  2  ?  of  3  ?  of    5  ?  of    7  ? 

7.  What  is  £  of  3  ?  of  5  ?  of    9  ?  of  14  ? 

8.  What  is  j  of  4  ?  of  6  ?  of  12  ?  of  18  ? 

9.  What  is  -i  of  5  ?  of  3  ?  of  20  ?  of  30  ? 

10.  What  is  TV  of  7  ?  of  9  ?  of  16  ?  of  47  ? 

11.  What  is  ^  of  4  ?  of  7  ?  of  11  ?  of  63  ? 

12.  What  is  ^  of   2?  of  7?  of  11?  of  34?  of  75? 

13.  What  is  ^  of  13?  of  9?  of  17?  of50?  of  91? 

14.  If  5  bushels  of  wheat  cost  $9,  what  will  1 
bushel  cost : 

ANALYSIS.  If  5  bushels  cost  $9,  1  bushel^  which  is  ^ 
of  5  bushels,  will  cost  I  of  $9  ;  I  of  $9  i*  $li.  There- 
fore,  if  5  bushels  cost  $9,  1  bushel  will  cost  $l£. 

15.  If  6  turkeys  are  worth  $5,  what  are  they 
worth  apiece  ? 

16.  If  you  divide  6  oranges  equally  among  7  boys, 
what  part  of  an  orange  will  each  receive  ? 

17.  If  a  man  travel  29  miles  in  9  hours,  how  far 
does  he  travel  in  1  hour  ? 

18.  If  1  man  can  build  a  barn  in  20  days,  in  what 
time  can  3  men  build  it  ? 

19.  If  a  horse  eat  5  bushels  of  oats  in  8  days, 
what  part  of  a  bushel  does  he  eat  in  1  day  ? 

20.  What  will  1  hat  cost,  if  4  hats  cost  $17  ? 


INTELLECTUAL   ARITHMETIC.  97 

62.     1.   What  are  f  of  3  ? 


ANALYSIS. 
of  1,  and  3 

|  of  3  are  3 
times  |   are  f 

times  j 
or  2|. 

« 

3;i*/ 
lerejore,  * 

\  of  I 

are  2| 

2. 

What 

are 

1 

of 

5? 

of 

4? 

of 

7? 

3. 

What 

are 

f 

of 

4? 

of 

5? 

of 

8? 

4. 

What 

are 

1 

of 

2? 

of 

3? 

of 

9? 

5. 

What 

are 

1- 

of 

3? 

of 

5? 

of 

10? 

of 

12? 

6. 

What 

are 

I8o" 

of 

4? 

of 

7? 

of 

15? 

of 

18? 

7. 

What 

are 

1 

of 

2? 

of 

3? 

of 

14? 

of 

20? 

8. 

What 

are 

1 

of 

5? 

of 

8? 

of 

19? 

of 

28? 

9. 

What 

are 

JL 

11 

of 

7? 

of 

13? 

of 

21? 

of 

30? 

10. 

What 

are 

f 

of 

2? 

of 

6? 

of 

15? 

of 

24? 

11. 

What 

are 

A 

of 

7? 

of 

36? 

of 

50? 

of 

63? 

12. 

What 

are 

1<L 

of 

35? 

of 

60? 

of 

77? 

of 

91? 

13. 

What 

are 

"A" 

of 

10? 

of 

15? 

of 

120? 

of 

150? 

14. 

If  4  cords 

of  wood  cost 

$14, 

what  will  5 

cords 

cost  ? 

ANALYSTS.  If  4  cords  of  wood  cost  $14,  5  cords 
will  cost  5  times  \  o/$14.  j  o/$14  is  $3^,  and  5  times 
$vM  are  $17-.|.  Therefore  5  cords  of  wood  will  cost 
$17J. 

15.  If  3  bushels  of  quinces  cost  $7,  what  will  2 
bushels  cost  ? 

16.  If  9  bushels  of  apples  cost  $4,  what  will  7 
bushels  cost  ? 

17.  At  6  cents  for  2  oranges,  how  many  oranges 
could  you  buy  for  21  cents  ? 

18.  If  4  men  can  do  a  piece  of  work  in  15  days, 
in  what  time  can  6  men  do  the  same  ? 

19.  If  a  quantity  of  provision  will  last  5  men  9 
days,  how  long  would  the  same  last  11  men  ? 

7 


98  INTELLECTUAL   ARITHMETIC.  [63. 

63.     1.    If  1  pound  of  butter  cost  19  cents,  what 
will  |  of  a  pound  cost  ? 

2.  A  barrel  of  beer  sold  for  $8  ;  what  was  |  of  it 
worth  ? 

3.  Sold  a  cow  for  $18,  which  was  only  £  of  her 
real  value  ;  what  was  her  real  value  ? 

4.  Bought  a  carriage    for    $65,  and    afterwards 
sold  it  for  |  of  what  it  cost  me ;  how  much  did  I 
gain  ? 

5.  A  farmer,  having  80  sheep,  sold  -^  of  them ; 
how  many  had  he  left  ? 

6.  If  I  give  4  pounds  of  butter,  worth  12-|-  cents  a 
pound,  for  8  pounds  of  sugar,  what  is  the  sugar 
worth  a  pound  ? 

7.  After  paying   |  of  my  money  for  a  piece  of 
land,  I  had  $48  left ;  how  much  money  had  I  at 
first? 

8.  A  man  bought  a  watch    and  chain  for  $50, 
which  was  £  of  what  the  watch  alone  cost ;  what  was 
the  cost  of  each  ? 

9.  If  a  man  can  cut  9  cords  of  wood  in  %  of  a 
week,  how  many  cords  can  he  cut  in  4  weeks  ? 

10.  A  man  paid  $35    for   a   book-case,   f   of   the 
cost  of  his  book-case  was  ^  of  what  he  paid  for  a 
bureau,  and  %  the  cost  of  the  bureau  was  ^  of  what 
he  paid  for  a  table  ;  what  did  he  pay  for  the  bureau, 
and  for  the  table  ? 

11.  If  4  quarts  of  chestnuts  cost  37  cents,  what , 
will  1  bushel  cost  ? 

12.  If  a  man  can  walk  7  miles  in  2  hours,  how 
far  can  he  walk  in  3  days,  by  walking  10  hours  a 
day? 

13.  If  |-  of  a  barrel  of  flour  is  worth  $8,  what  are 
12  barrels  worth  ? 

14.  If   3  pecks  of  grass-seed   cost  14   shillings, 
what  will  4  quarts  cost  ? 


63.]  INTELLECTUAL   ARITHMETIC.  99 

15.  If  3  yards  of  silk  cost  $19J,  what  will  7  yards 
cost? 

16.  If  a  man  earn  $32|-  in  4  weeks,  how  much  will 
he  earn  in  2  weeks  ? 

17.  If    $9  will  buy  4f  yards  of  cloth,  how  much 
will  $1  buy  ? 

18.  A  man,  having  56|  acres  of  land,  sold  |  of  it ; 
how  many  acres  did  he  sell  ? 

19.  If  9  horses  eat  5|  bushels  of  oats  in  a  day, 
how  many  bushels  will  4  horses  eat  in  the  same  time  ? 

20.  If  3  yards  of  flannel  cost  $|,  what  will  8 
yards  cost  ? 

21.  If  10  bushels  of  wheat  are  worth  22|  bushels 
of  corn,  how  many  bushels  of  corn  are  3  bushels  of 
wheat  worth  ? 

22.  If  14  acres  of  meadow  land  produce  32 1  tons 
of  hay,  how  many  tons  will  5  acres  of  the  same  land 
produce  ? 

23.  A  cistern  is  filled  by  3  pipes  in  6-f  hours  ;  how 
many  pipes  of  the  same  size  will  be  requirecTlo  fill  it 
in  ^  of  an  hour  ? 

24.  A  boy  sold  5  quarts  of  strawberries  at  the  rate 
of  3  quarts  for  13  cents  ;  how  much  did  he  receive 
for  the  whole  ? 

25.  A  tailor  bought  3  pieces  of  cassimere,  each 
piece  containing  6|  yards,  for  $48-^ ;  how  much  did 
it  cost  a  piece,  and  how  much  a  yard  ? 

26.  If  a  pole  8  feet  long  cast  a  shadow  6  feet,  how 
long  is  a  pole  that  casts  a  shadow  12}  feet  at  the 
same  time  ? 

27.  How  much  less  than  $17  will  9  yards  of  satin 
cost,  if  2  yards  cost  $3^  ? 

28.  If  3  yards  of  velvet  cost  $5J,  how  much  more 
than  $9  will  6  yards  of  it  cost  ? 

29.  If  a  horse  travel  40|-  miles  in  6  hours,  how 
far  will  he  travel  in  4  hours  ? 


100  INTELLECTUAL   ARITHMETIC.  [64. 

64.     1.   If  5  pounds  of  chalk  cost    28 -|   cents, 
what  will  |  of  a  pound  cost? 

2.  If  3  pairs  of  socks  cost  (j^,  how  many  pairs 
can  be  bought  for  $2^  ? 

3.  Lucas  is  f  as  old  as  his  father,  who  is  60  years 
of  age  ;  what  is  Lucas's  age  ? 

4.  If  £  of  a  box  of  raisins  cost  $2-^,  what  will  £ 
of  a  box  cost  ? 

5.  A  boy  sold  some  peaches  for  §|  cents,  at  the 
rate  of  3  for  4£  cents  ;  how  many  did  he  sell  ? 

6.  If  7  bushels  of  oats  cost  $lf ,  what  will  12f 
bushels  cost  ? 

7.  If  2 1  yards  of  shalloon  cost  $4£,  what  will  5 
yards  cost  ? 

8.  Bought  4J  barrels  of  cider  at  $3|  a  barrel,  and 
paid  in  wood  at"  $3  a  cord  ;  how  many  cords  of  wood 
paid  for  the  cider  ? 

9.  John  has  $5|,  and  Gilbert  has   If    times   as 
much  ;  how  much  has  Gilbert  ? 

10.  Three  men  incur  an  expense  of   $27|- ;  how 
much  more  than  $7-|  must  each  pay  ? 

11.  A  man,  being  asked  his  age,  said  that,  were  he 
3  times  as  old,  y1^  of  his  age  would  be  8  years ;  how 
old  was  he  ? 

12.  If  a  pound  of  tea  is  worth  3^  times  as  much 
as  a  pound  of  coffee,  what  will  6|  pounds  of  coffee 
cost,  when  tea  is  worth  50  cents  a  pound  ? 

13.  If  2f  poiinds  of  cheese  cost  20  cents,  what 
will  12  pounds  cost  ? 

14.  If  34-  barrels  of  apples  cost  $51,  what  will  | 
barrel  cost  ? 

15.  A  stone  mason  worked  llf  days,  and  after 
paying  his  board  and  other  expenses  with  f  of  his 
earnings,  had  $20  left ;  how  much  did  he  receive  a 
day? 


64.]  INTELLECTUAL   ARITHMETIC.  101 

16.  If  7  bushels  of  potatoes  cost  $3|-,  how  many 
bushels  can  be  bought  for  $14|  ? 

17.  If  J  of  a  quart  of  braiicly  cost  $f ,  how  many 
gallons  will  $12f  buy  ? 

18.  How  many  yards  of  silk  can  be  bought  for  80 
shillings,  if  3  shillings  be  paid  for  f  of  a  yard  ? 

19.  If  |  of  a  shilling  will  buy  $  of  a  pound  of 
butter,  how  many  pounds  will  7  shillings  buy  ? 

20.  How  many  gallons  of  molasses  can  be  bought 
for  $31,  if  |  of  a  gallon  cost  $-}-  ? 

21.  How  many  oats  can  be  bought  for  10  shillings, 
if  9  bushels  cost  24  shillings  ? 

22.  If  5  dozen  of  eggs  cost  4|  shillings,  how  many 
dozen  can  be  bought  for  7  shillings  ? 

23.  If  8  yards  of  velvet  ribbon  cost  $!-£,  how  many 
yards  can  be  bought  for  $3^-  ? 

24.  How  many  pints  of  alcohol  will  3  shillings 
buy,  if  •£  of  a  pint  cost  ^  of  a  shilling  ? 

25.  If  a  man  eat  If  pounds  of  bread  in  a  day,  how 
many  days  will  221  pounds  last  him  ? 

26.  How  many  pounds  of  sugar  worth  10  cents  a 
pound  can  be  had  for  6|  pounds  of  cheese  worth  7^ 
cents  a  pound  ? 

27.  If  a  horse  consume  8 \  bushels  of  oats  in  3 
weeks,  how  many  bushels  would  he  consume  in  5 
weeks  ? 

28.  A  man  gave  6|-  pounds  of  butter  at  12  cents 
a  pound  for  |  of  a  gallon  of  oil ;  what  was  the  oil 
worth  a  gallon  ? 

29.  When  4  pounds  of  tea  can  be  bought  for  $2|, 
how  much  can  be  bought  for  $T^-  ? 

30.  A  man,  having  $10,  gave  f  of  his  money  for 
clover  seed  at  $3J  a  bushel ;  how  much  did  he  buy  ? 

31.  If  I  of  a  bushel  of  rye  cost  $|,  how  many 
bushels  can  be  bought  for  $7  ? 


102  INTELLECTUAL   ARITHMETIC.  [6*5. 

63.     1.    If  £  a  yard  of  cloth  cost  $|,  what  will  £ 
of  a  yard  cost  ? 

2.  If  ^  of  2  pounds  of  tea  cost  $1|,  what  will  | 
of  1  pound  cost? 

3.  What  will  -|  of  a  barrel  of  apples  cost,  if  |  of 
a  barrel  cost  $f-  ? 

4.  If  |  of  a  pound  of  butter  is  worth  i  of  a  pound 
of  fish,  how  many  pounds  of  fish  are  l|  pounds  of 
butter  worth  V 

5.  What  will  be  the  cost  of  6  barrels  of  flour  at 
the  rate  of  $2  f  for  every  |  of  a  barrel  ? 

6.  At  $1  a  quart,  what  part  of  a  bushel  of  clover 
seed  can  be  bought  for  $3^  ? 

7.  Since  I  was  25  years  old,  f  of  my  entire  age 
has  passed  ;  what  is  my  age  ? 

8.  A  man,  engaging  in  play,  lost  ^  of  his  money, 
after  which  he  gained  $75,  when  he  found  that  he 
had  $375  ;  how  much  money  did  he  lose  ? 

9.  If  4  horses  consume  2|  bushels  of  oats  in  2J 
days,  how  many  bushels  will  6  horses  consume  in 
the  same  time  ? 

10.  If  I  of  a  bushel  of  barley  be  given  for  f  of  a 
bushel  of  corn  worth  $f  a  bushel,  what  is  the  barley 
worth  a  bushel  ? 

11.  A  person  having  a  drove  of  turkeys,  after  sell- 
ing 35,  found  that  he  had  -|  of  his  drove  left ;  how 
many  turkeys  in  his  drove  at  first  ? 

12.  What  number  is  that  to  which  if  |  of  itself 
be  added,  the  number  will  be  55  ? 

13.  Wl;at  number  added  to  3  times  |  of  27  will 
make  the  number  40  ? 

14.  If  24  is  |-  of  some  number,  what  is  ^  of  the 
same  number  ? 

15.  What  number  taken  from  2^  times  12|  will 
leave  20f  ? 


6«5.]  INTELLECTUAL   ARITHMETIC.  103 

16.  If  $40  exceed  by  $10,  J  of  f  of  what  I  gained 
in  the  sale  of  a  house  and  lot,  how  much  did  I  gain  ? 

17.  If  I  of  4  tons  of  coal  cost  $5£,  what  will  |  of 
2  tons  cost  ? 

18.  A  young  lady,  being  asked  her  age,  replied 
that  5  times  ^  of  30  years  was  4|  years  more  than  8 
times  her  age  ;  what  was  her  age  ? 

19.  In  an  orchard,  ^  the  trees  bear  apples,  1  bear 
peaches,  -^  bear  pears  and  15  trees  bear  plums; 
how  many  trees  in  the  orchard,  and  how  many  of 
each  kind  ? 

20.  How  many  yards  of  cloth  that  is  |  of  a  yard 
wide  are  equal  to  12  yards  |  of  a  yard  wide  ? 

21.  A,  B,  and  C  can  do  a  piece  of  work  in  5  days  ; 
B  and  C  can  do  it  in  8  days ;  in  what  time  can  A  do 
it  alone  ? 

22.  A  can  build  a  piece  of  wall  in  3  days,  and  B 
can  build  it  in  4  days ;  in  what  time  can  both  build 
it  together  ? 

23.  If  |  the  value  of  a  carriage  is  equal  to  f  the 
value  of  a  horse,  and  the  difference  in  their  values  is 
$25,  what  is  the  value  of  each  ? 

24.  A  tailor  paid  $73,  which  was  -^  of  all  the 
money  he  had,  for  cloth,  at  the  rate  of  $3  a  yard ; 
how  many  yards  could  he  have  purchased  with  all 
his  money,  at  the  same  rate  ? 

25.  A  father  divided  a  piece  of  land  among  his  3 
sons  ;  to  the  first  he  gave  10J  acres,  to  the  second  | 
of  the  whole,  and  to  the.  third  as  much  as  to  the 
other  two  ;  how  many  acres  had  each  ? 

26.  A  farmer  bought  2  cows  for  $56,  paying  |  as 
much  for  one  as  for  the  other ;  how  much  did  each 
cost  him  ? 

27.  A  and  B  can  do  a  piece  of  work  in  14  days ; 
A  can  do  f  as  much  as  B ;  in  how  many  (lays  can 
each  do  it  ? 


104  INTELLECTUAL   ARITHMETIC.  [66. 

66.     1.   16  is  I  of  what  number  ? 

ANALYSIS.  16  is  |  of  5  times  \  of  16  ;  j  of  16  is  4, 
and  5  fo'mes  4  are  20.  Therefore,  16  2*5  i  o/"20. 

Or  thus :  Since  16  zs  f  of  some  number,  J  o/*  ^e  number, 
which  is  £  of  %,  is  £  of  16,  or  4; ;  and  4  zs  £  o/  5  fr'wes  4^ 
or  20.  Therefore,  $c. 


2. 

42 

is 

f 

of 

what 

number  ? 

3. 

25 

is 

* 

of 

what 

number  ? 

4. 

16 

is 

£ 

of 

what 

number  ? 

5. 

32 

is 

t 

of 

what 

number  ? 

6. 

60 

is 

A 

of 

what 

number  ? 

7. 

14 

is 

I 

of 

what 

number  ? 

8. 

48 

is 

1 

of 

what 

number  ? 

9. 

75 

is 

1 

of 

what 

number  ? 

10. 

84 

is 

J| 

of 

what 

number  ? 

11. 

55 

is 

ii 

of 

what 

number  ? 

12. 

64 

is 

A 

of 

what 

number  ? 

13. 

13 

is 

I 

of 

what 

number  ? 

14. 

18 

is 

i 

of 

what 

number  ? 

15. 

28 

is 

1 

of 

what 

number  ? 

16. 

40 

is 

of 

what 

number  ? 

17. 

54 

is 

A 

of 

what 

number  ? 

18. 

10 

is 

~15 

of 

what 

number  ? 

19. 

12* 

is 

% 

of 

what 

number  ? 

20. 

15f 

is 

f 

of 

what 

number  ? 

21. 

19  1 

is 

1*0 

of 

what 

number  ? 

22. 

24f 

is 

A 

of 

what 

number  ? 

23. 

16^ 

is 

of 

what 

number  ? 

24. 

J 

is 

1 

of 

what 

number  ? 

25. 

i 

is 

f 

of 

what 

number  ? 

26. 

A 

is 

! 

of 

what 

number  ? 

67.]  INTELLECTUAL   ARITHMETIC.  105 

67.     1.    24  is  I  of  how  many  times  10  ?  * 

ANALYSIS.  24  is  f  of  as  many  times  10  as  10  is  con- 
tained times  in  5  times  \  of  24  ;  \  of  24  £s  6,  and  5 
tfmes  6  £s  30;  10  is  contained  in  30,  3  times.  There- 
fore 24  is  ^  of  3  times  10. 

2.  18  is   I  of  how  many  times    6  ? 

3.  25  is   |  of  how  many  times  15  ? 

4.  36  is  -|  of  how  many  times    4  ? 

5.  28  is  y7g  of  how  many  times    8  ? 

6.  40  is  T52  of  how  many  times  16  ? 

7.  75  is  |  of  how  many  times  20  ? 
S.  64  is  -|  of  how  many  times  24  ? 

9.  48    is  if  of  how  many  times  J  of  30  ? 

10.  35  .is  |  of  how  many  times  j  of  28  ? 

11.  42    is-^  of  how  many  times  ^  of  63  ? 

12.  84    is  ^  of  how  many  times  |  of  35  ? 

13.  27    is  T9g  of  how  many  times  £  of  72  ? 

14.  36    is   |  of  how  many  times  J  of  21  ? 

15.  14|  is  |   of  how  many  times  ^  of  20  ? 

16.  16 1  is  J  of  how  many  times  ^  of  54  ? 

17.  12f  is  ^  of  how  many  times  J  of  40  ? 

18.  I  is  |   of  how  many  times  ^  of    J  ? 

19.  £  Of  |  is  |  Of  how  many  times  |-  of  15  ? 

20.  James  gave  56  cents  for  a  pair  of  skates,  which 
was  ^  of  what  he  gave  for  his  sled  ;  what  did  his 
sled  cost  him  ? 

21.  A  farmer  paid  $23^  for  a  cow,  which  was  | 
of  what  he  received  for  a  horse  ;  what  was  the  dif- 
ference in  the  price  of  the  cow  and  the  horse  ? 

22.  A  man  sold  4J  cords  of  wood  at  $2|-  a  cord, 
which  was  |  of  what  he  received  for  a  ton  of  hay ; 
how  much  did  he  receive  for  the  hay  ? 

*  Please  turn  to  67  in  the  Appendix,  page  170. 


100  INTELLECTUAL   ARITHMETIC.  [68, 

23.   Paid  $£  for  a  cravat,  which  was  f  of  what  I 
paid  for  a  vest ;  what  was  the  cost  of  the  vest  ? 

•  24.  A  gentleman  bought  a  sleigh  for  $50,  which 
was  -|  of  '6  times  what  he  paid  for  a  harness ;  what 
did  the  harness  cost  him  ? 

25.  A  lady  bought  a  fur  cape  for  $90,  which  was 
l£-  of  what  she  paid  for  12  yards  of  silk  ;  what  was 
the  cost  of  the  silk  a  yard  ? 

26.  A  merchant  sold  5  barrels  of  flour  for  $324, 
which  was  f  of  what  he  received  for  all  he  had  left, 
at  $4  a  barrel ;  how  many  barrels  in  all  did  lie  sell  ? 


68.     1.   |  of  20  is  how  many  thirds  of  24  ? 

ANALYSIS.  |  of  20  is  as  many  thirds  of  24  as  \  of 
24  is  contained  times  in  4  times  £  of  20.  ^  ^  of  20  is  4, 
and  4  times  4  is  16  ;  8  is  contained  in  16,  2  times. 
Therefore,  $  of  20  is  |  of  24. 

2.  -|  of    56  is  how  many  fourths  of  28  ? 

3.  |  of    64  is  how  many  fifths  of  60  ? 

4.  I  of    48  is  how  many  sevenths  of  28  ? 

5.  |  of  108  is  how  many  fourths  of  32  ? 

6.  ^  of    90  is  how  many  twelfths  of  84  2 

7.  TJL  of  160  is  how  many  thirds  of  36  ? 

8.  ^  of  100  is  how  many  fifteenths  of  30  ? 

9.  |  of  lOf  is  how  many  sixths  of  12  ? 

10.  I  of  37f  is  how  many  tenths  of  40  ? 

11.  f  of  42|  is  how  many  ninths  of  72  ? 

12.  -£  of  78|  is  how  many  thirds  of  9  ? 

13.  f  of  28^  is  how  many  halves  of  38  ? 

14.  11  Of    42  is  how  many  fourths  of  44  ? 

15.  ^  of    96  is  how  many  fifths  of  90  ? 
lt>.  Xi  of    40  is  how  many  ninths  of  72  ? 


69.]  INTELLECTUAL   ARITHMETIC.  10? 

69.     1.    §  of  24  is  I  of  what  number  ? 

ANALYSIS.  §  of  24  &  |  o/*3  ^'raes  i  o/  5  ft'me*  J  of 
24  ;  I  of  24  ?',9  4,  *5  times  4  i's  20  ;  i  o/  20  *a  10,  and  3 
tfmes  10  &  30.  Therefore  |  o/  24  is  f  o/  30. 

2.  |-  of    56  is  T7Q-  of  what  number  ? 

3.  _4_  Of    88  is   ^   of  what  number  ? 

4.  f  of  36  is  T35-  of  what  number  ? 

5.  |  of  27  is   f    of  what  number  ? 

6.  _7_  Of  go  is  T43-  of  what  number? 

7.  f  of  52  is   |    of  what  number  ? 

8.  I  of  81  is  T9o  of  what  number  ? 

9.  f  of  63  is   I   of  what  number  ? 

10.  |  of  100  is  If  of  what  number  ? 

11.  TYg  of    96  is  y\  of  what  number  ? 

12.  |  of  f  of  64  is   |   of  what  number? 

13.  |  of  |-  of  75  is  {f  of  what  number  ? 

14.  |  of  |  of  56  is   ^   of  f  of  what  number  ? 

15.  4  of  *  of  72  is   i   of  4  of  what  number  ? 

-J  O 

16.  I-  of  f  of  36  is   -I   of  A  of  what  number  ? 

25  .   u  O  ^j 

17.  |  of  35  is  -|  of  how  many  times  7  ? 

ANALYSIS.  |  o/*  35  is  ^  of  as  many  times  7  as  7  e^ 
contained  times  in  8  times  \  of  3  times  %  of  35  ;  ^.  q/' 
3o  &  5,  cm<7  3  i5/mes  5  £s  15  ;  4  o/  15  fs  3,  a/^/8  times  3  ?'s 
24  ;  7  is  contained  in  24  3  1  fo'mes.  Therefore,  f  o/  35 

7. 


18.  -^  of    54  is   |   of  how  many  times  5  ? 

19.  f  of     24  is  -^  of  how  many  times  12  ? 

20.  f  of    75  is  T9¥  of  how  many  times  8  ? 

21.  i  of    56  is   ^    of  how  many  times  20  ? 

22.  f  of  108  is   f    of  how  many  times    9  ? 


108  INTELLECTUAL   ARITHMETIC.  [7O. 

of  121  are  f  of  how  many  times  7  ? 

of    33  are  |  of  how  many  times  6? 

of    34  are  f  of  how  many  times  14  ? 
|  of    30  are  ff  of  how  many  times  20  ? 
|-  of  ^  of  63  are  ^  of  |  of  how  many  times  11  ? 
I  of  I  of  50  are  |  of  f  of  how  many  times  8  t 


7O.     1.    f  of  56  are  |  of  3  times  what  number  ?  * 

ANALYSIS.  $  of  56  are  -§  q/*  3  rime*  £  o/  9  riwe*  £ 
o/  4  rimes  4  o/  50  ;  j  o/  56  is  8,  cwd  4  times  8  t*  32  ; 
£  o/  32  a*  4,  and  9  times  4  -w  36  ;  ^  o/36  ^  12.  Tftere- 
fore,  4  <^/  56  are  f  o/  3  rimes  12. 

2.  |  of    45  are  f  of    6  times  what  number  ? 

3.  |  of    64  are   |  of    9  times  what  number  ? 

4.  |-  of    63  are  -^  of    4  times  what  number  ? 

5.  §  of    36  are  ^  of    5  times  what  number  ? 

6.  ^4T  of  110  arc  f  of    8  times  what  number  ? 

7.  -j£  of    80  are  %  of  11  times  what  number  ? 

8.  |  of    72  are  ^  of    5  times  what  number  ? 

9.  |  of    81  are  ||  of  10  times  what  number  ? 

10.  I  of    21  are  |  of    8  times  what  number  ? 

11.  4  of    14  are  i   of    3  times  what  number  ? 

o  I 

12.  |  of  |  of  70  are  ^  of  4  times  what  number  ? 

13.  A  man,  being  asked  his  age,  answered  that  if 
he  were  3  times  as  old,  \  of  his  age  would  be.  24 
years ;   how  old  was  he  ? 

14.  A  gentleman  divided  his  farm  between  his  2 
sons,  giving  the  elder  10  acres  more  than  |  of  the 
whole,  and  the  younger  the  remainder,  which  was  22 
acres  more  than  \  of  the  whole ;  how  many  acres  in 
the  farm  ? 

*  See  70  in  the  Appendix,  page  170. 


7O.]  INTELLECTUAL   ARITHMETIC.  109 

15.  A  coal  merchant  sold  |  of  what  coal  he  had 
on  hand  for  $90,  at  the  rate  of  $6  a  ton  ;  how  many 
tons  had  he  ? 

16.  Bought  a  piano  for  $300,  and  f  of  the  cost  of 
the  instrument  was  |  of  what  I  received  of  9  young 
ladies  for   its   use  one  year;   how  much   did   each 
young  lady  pay  for  its  use  ? 

17.  The  tools  in  a  shop  are  w^orth  $80  ;  f  of  this 
is  f  of  £  of  2  times  the  value  of  the  stock ;  what  is 
the  v^lue  of  the  stock  ? 

18.  A  peddler,  after  selling  $200  worth  of  his  stock 
in  trade,  finds  that  |  of  the  remainder  is  equal  to  | 
of  3  times  the  amount  sold ;  what  amount  of  stock 
had  he  at  first  ? 

19.  A  merchant,  after  selling  from  a  cask  of  wine 
15  gallons  more  than  |  of  the  whole,  found  that  the 
number  of  gallons  left  was  just  3  times  the  number 
of  gallons  sold ;  how  many  gallons  did  the  cask  con- 
tain at  first  ? 

20.  If  a  store  be  worth  $1000,  and  -f  of  the  value 
of  the  store  be  equal  to  -f  of  2  J  times  the  value  of  the 
goods  it  contains,  what  is  the  value  of  the  goods  ? 

21.  Two  boys,  comparing  their  money,  one  said 
he  had  50  cents ;  the  other  said,  "  -£$  of  your  money 
is  just  -f%  of  6  times  my  money ; "  how  many  cents 
had  the  latter  boy  ? 

22.  The  distance  from  Boston  to  Albany  is  200 
miles,  and  |-  of  this  distance  is  |  times  J  the  distance 
from  Albany  to  Niagara  Falls,  lacking  5  miles ;  wha* 
is  the  distance  from  Boston  to  Niagara  Falls  ? 

23.  The  distance  from  Chicago   to  Alton  is  268 
miles,  and  -|  of  this  distance  plus  15  miles,  is  4^  times 
|  of  the  distance  from  Alton  to  St.  Louis ;  what  is 
the  distance  from  Chicago  to  St.  Louis  ? 

24.  40  is  |  of  f  of  £  of  8  times  what  number  ? 


110  INTELLECTUAL   ARITHMETIC. 

71.     1.    |  of  35  is  I  of  how  many  thirds  of  18  ?  * 

ANALYSIS.  Of  as  many  thirds  of  18  as  ±  of  18  is 
contained  times  in  9  times  i  of  4  times  4  of  35  ;  4  ^/' 
35  £s  5,  and  4  fa'mes  5  is  20 ;  ±  of  20  £s  4,  and  9  fames  4 
•*'s  36 ;  \  of  18  is  6,  twd  6  /s  contained  in  36,  6  fa'mes* 
Therefore,  $  of  35  z's  f  o/  6  tfwVds  o/  18. 

2.  |  of   42  is   *  of  how  many  fifths  of  35  ? 

3.  |  of    96  is   |  of  how  many  eighths  of  24  ? 

4.  |  of  180  is  §  of  how  many  tenths  of  50  ? 

5.  |-  of    84  is  |  of  how  many  sixths  of  48  ? 

6.  -fa  of  100  is  -^Q  of  how  many  ninths  of  45  ? 

7.  ^  of   45  is  ^.j  °f  now  many  halves  of  48  ? 

8.  ^T  of    77  is  -£  of  how  many  twelfths  of  72  ? 

9.  -\l  of    30  is  f  of  how  many  thirds  of  21  ? 

10.  -&  of    28  is  2%  of  how  many  fourths  of  24  ? 

11.  |  of    18  is  -/T  of  how  many  twelfths  of  60  ? 

12.  I  of    80  is  §  of  how  many  fourths  of  40  ? 

13.  |   of    42  is  T9T  of  how  many  eighths  of  72  ? 

14.  ^  of    39  is  23^  of  how  many  ninths  of  180  ? 

15.  f  of  |  of  18  is  4  times  what  part  of  35  ? 

ANALYSIS..  Such  a  part  o/*  35,  as  35  as  contained 
times  in  \  of  5  times  ^  of  6  times  4  of  18  ;  \  of  18  is 
6,  and  6  times  6,  zs  36  ;  ^  of  36  ^s  4,  and  5  ft'mes  4  ^s 
20  ;  |  of  20  i's  5,  and  35  es  contained  in  5,  g5^  or  ^ 
times.  Therefore  |  o/*  |  o/1  18  is  4  times  %>  or  %,  of  35. 

16.  |  of  |  of    40  is  3  times  what  part  of  24  ? 

17.  |  of  f  of    49  is  2  times  what  part  of  28  ? 

18.  -i-  of  T9^-  of  100  is  9  times  what  part  of  25  ? 

19.  f  of  I  of   48  is  7  times  what  part  of  35  ? 

20.  •£$  of  |  of    60  is  7  times  what  part  of  64  ? 

21.  f  of  |  of    80  is  3  times  what  part  of  96  ? 

*  Observe  the  "  changes  "  in  the  Appendix,  719  page  171. 


7£.]  INTELLECTUAL   ARITHMETIC.  Ill 

72.     1.    I  of  36  is  4  of  how  many  times  f  of  42  ?* 

ANALYSIS.  Of  as  many  times  f  of  42  as  2  ^'raes  | 
o/*  42  ?s  contained  times  in  9  ft'mes  |  of  4  £w?es  ^  q/ 
36  ;  -J  o/"  36  is  12,  «>?<#  4  ^'mes  12  is  48  ;  j  of  48  w  12, 
«??r?  9  times  12  *s  108  ;  4  of  42  ?'.<?  6,  and  2  tfmes  6  ^s 
12,  and  12  ?*s  contained  in  108,  9  ta'mes.  Therefore  \ 
.of  36  /*  |  of  9  tfwie*  f  o/  42. 


2.  I  of    64  is   I  of  how  many  times  |  of  15  ? 

3.  |  of    27  is  |   of  how  many  times  f  of  56  ? 

4.  -§•  of    81  is  |  of  how  many  times  \  of  28  ? 

5.  f  of    50  is  ||-  of  how  many  times  |  of  60  ? 

6.  |  of    36  is  ^  of  how  many  times  \  of  27? 

7.  f  of    32  is  ^  of  how  many  times  ^  of  45  ? 

8.  T^  of  150  is  |  of  how  many  times  f  of  40  ? 

9.  |   of  108  is  -£$  of  how  many  times  f  of  16|  ? 

10.  -fy  of    65  is  ^  of  how  many  times  ^  of  ^  of  50  ? 

11.  |  of    60  is  -|  of  how  many  times  f  of  25  ? 

12.  |  of    72  is  §  of  how  many  times  -|-  of  |  of  70  ? 

13.  §  of  J  of  84  is  |  of  how  many  times  ^  of  f 
of  96? 

14.  A  of  f  of  90  is  ±  of  f  of  how  many  times  f 
of  |  of  20  ? 

15.  ^  of  |^  of  36  is  ^  of  -|  of  how  many  times  | 
of  f  of  120  ? 

16.  A  man  pays  $400  rent,  and  |  of  this  is  just  f 
of  -|-  of  twice  his  annual  income  ;  what  is  his  annual 
income  ? 

17.  A  boy  being  asked  his  age  said  that  18  years  was 
2  years  less  than  f  times  |  of  his  age  ;  how  old  was  he  ? 

18.  The   distance    from    Baltimore    to    Washington 
is  39  miles;  if  5  miles  be  subtracted   from  §  of  this 

For  "  changes  "  see  Appendix,  72,  page  178. 


112  INTELLECTUAL   ARITHMETIC.  [72. 

distance,  the  remainder  will  be  f  times  \  the  distance 
from  Philadelphia  to  Baltimore  ;  what  is  the  distance 
from  Philadelphia  to  Washington  ? 

19.  Mr.  13.,  who  is  64  years  of  age,  is  2f  times  as 
old  as  his  eldest  son,  and  his  eldest  son  is  2£  times 
as  old  as  his  youngest  brother  ;  what  is  the  difference 
in  the  ages  of  the  two  brothers  ? 

20.  Oscar  earned  a  certain  number  of  pennies ; 
Rufus  earned  *  as  many  minus  4,    and  David  earned 
|  as  many  as  Rufus,  plus  7 ;  Oscar  earned  50  pen- 
nies ;  how  many  did  Rufus  and  David  earn  ? 

21.  A  man  put  his  money  into  4  packages  ;  in  the 
first  he  put  f ,  in  the  second  ^,  in  the  third  -J,  and  in 
the  fourth  $24  ;  how  much  money  had  he  ? 

22.  A  sold  |  of  his  sheep  on  Monday ;  Tuesday 
he  bought  f  as  many  as  he  had  sold  ;  he  then  had  60 
sheep  ;  how  many  had  he  at  first  ? 

23.  Mrs.  D.'s  shawl  cost  $30  ;  |  of  the  cost  of  the 
shawl  was  f  of  6  times  the  cost  of  her  dress ;  what 
was  the  cost  of  her  dress  ? 

24.  B  and  C  engaging  in  play,  B  had  f  as  much 
money  as  C  ;  C  gained  $16,  which  was  |  of  1|-  times 
as  much  as  he  commenced  with  ;  how  much  did  he 
commence  with,  and  how  much  had  B  left  ? 

25.  A  farmer,  being  asked  how  many  sheep  he 
had,  replied  that  he  had  just  sold  150,  and  that  -|  the 
number  he  had  sold  was  6  times  |  of  what  he  had 
left ;  how  many  had  he  left  ? 

26.  Mr.  S.  gave  J  of  1-^  times  his  ready  money  for 
a  buggy,  -|  of  what  was  left  for  a  harness,  and  had 
$12  remaining ;  what  did  he  pay  for  the  buggy  ? 

27.  A  paid  $4800  for  his  farm ;  f  of  this  is  4J 
times  f  of  2  times  what  it  cost  to  build  the  house ; 
what  was  the  cost  of  the  house  ? 

28.  1  of  f  of  80  is  I-  of  I  of  how  many  times  | 
of  4  of  100  ? 


73.]  INTELLECTUAL   ARITHMETIC.  113 

CHAPTER  VII. 
RATIO    AND     PROPORTION. 

73.     1.   What  part  of  4  is  1  ?  of  4  is  3  ?  * 

ANALYSIS.  Since  1  is  %  of  4,  3  must  be  3  times  £  part 
of  4,  or  £  of  4.  Therefore  3  t*  f  of  4. 

2.  What  part  of    3  is    1  ?  of    3  is    2  ? 

3.  What  part  of    7  is    1  ?  of    5  is    3  ? 

4.  What  part  of    8  is    2  ?  of    9  is    5  ? 

5.  What  part  of  10  is    7  ?  of  13  is    9  ? 

6.  What  part  of    8  is    9  ?  of  12  is    7  ? 

7.  What  part  of  16  is  11  ?  of  20  is  17  ? 

8.  What  part  of  40  is    9  ?     What  is  the  ratio  ? 

9.  What  part  of  30  is  27  ?     What  is  the  ratio  ? 

10.  What  part  of     £  is    f  ?     What  is  the  ratio  ? 

ANALYSIS,  f  =  |f ,  and  §  —  |f ;  the  ratio  of  fg-  to 
|-|  is  the  same  as  that  of  their  numerators,  10  to  12  :  what 
vart  of  12  is  10  ?  -JJ  —  I-  Therefore  f  is  {  of  fa  and  th* 
ratio  is  £. 

11.  What  part  of  £  is  £  ?  of  f  is  J  ? 

12.  What  part  of   |  is  f  ?  of  ^  is  £  ? 

13.  What  part  of  f  is  f  ?  of  T\  is  f  ? 

14.  What  part  of  ^  is  f  ?  of  |-  is  f  ? 

15.  What  part  of  ^  is  f  ?     What  is  the  ratio  ? 

16.  What  part  of  5    is  f  ?     What  is  the  ratio  ? 
1J.  What  part  of  7    is  f  ?  of  3^  is  2  ? 

18.  What  part  of  4|  is  f  ?  of  7^  is  3J  ? 

19.  What  part, of    f  is  2  ?  of  2|  is  If  ? 

20.  What  part  of  -^  is  5  ?  of    f  is  6  ? 

*  The  quotient  arising  from  dividing  one  number  by  another  is  called 
the  ratio.  Thus,  what  part  of  4  is  1  ?  It  is  1  divided  by  4,  equal  to  ^,  the 
ratio.  What  part  of  4  is  3  ?  It  is  3  divided  by  4,  equal  to  |,  the  ratio. 


114  INTELLECTUAL   ARITHMETIC.  [74. 

74.  1.  What  part  of  25  dollars  is  5  dollars  ?  is 
10  dollars  ? 

2.  What  part  of  16  pounds  is  4  pounds  ?  is  7 
pounds  ?  is  12  pounds  ? 

8.  What  part  of  1  bushel  is  1  peck  ?  is  2  pecks 
and  4  quarts  ?  is  6  quarts  ? 

4.  What  part  of  1  pound  is  12  shillings  ? 

5.  What  part  of  1  dollar  is  20  cents  ?  is  5  dimes  ? 

6.  What  part  of  1  cwt.  are  15  pounds  ? 

7.  What  part  of  1  cwt.  are  6  Ibs.  ?  9  Ibs.  ? 

8.  What  part  of  1  ton  is  14  cwt.  ?  15  cwt.  ?  18  cwt.  ? 

9.  What  part  of  3  pounds  is  10  oz.  ?  is  1  Ib.  6  oz.  ? 

10.  What  part  of  1  foot  is  3  in.  ?  10  in.  ?  11  in.  ? 

11.  What  part  of  2  yds.  is  1  foot  ?  1  foot  10  inches  ? 

12.  What  part  of  1  mile  is  3  furlongs  ?  5  furlongs 
20  rods  ? 

13.  What  part  of  1  mile  is  140  rods  ?  160  rods  ? 

14.  What  part  of  1  gallon  is  1  quart  ?  1  pint  ? 

15.  What  part  of  1  hhd.  is  5  gallons  ?  21  gallons  ? 

16.  What  part  of  1  quart  is  1  pint  ?  2  gills  ? 

17.  What  part  of  1  hour  is  15  minutes  ?  40  min- 
utes ? 

18.  What  part  of  1  day  is  3  hours  ?  8  hours  ?  16 
hours  ? 

19.  What  part  of  3  weeks  is  2  days  ?  5  days  ?  9 
days? 

20.  What  part   of  1  year  is  3  weeks  ?  7  weeks  ? 

21.  What  part  of  5  pounds  6  ounces  is  3  pounds 
10  ounces  ? 

22.  What  part  of  3  hhd.  is  1  hhd.  22  gallons  ?  , 

23.  What  part  of  1  mile  3  fur.  is  4  fur.  20  rods  ? 

24.  What  part  of  3  pecks  is  6  quarts  1  pint  ? 

25.  Two  pounds  is  what    part   of  1  cwt.  ?  of  2 
cwt.  ? 

26.  Eight  inches  is  what  part  of  a  foot  ?  of  2  feet  ? 
of  1  yard  ?  of  4  yards  ? 


74.]  INTELLECTUAL   ARITHMETIC.  115 

27.  Three  quarts  is  what  part  of  a  gallon  ?  of  5 
gallons  ?  of  10  gallons  ?  of  1  hhd.  ? 

28.  What  part  of  9  miles  is  |  of  8  miles  ? 

29.  AVhat  part  of  4£  acres  is  |  of  3£  acres  ? 

SO.  A  man,  having  $15,  gave  $3£  lor  a  hat,  and 
$4 1-  for  a  pair  of  boots  ;  what  part  of  his  money  did 
he  use,  and  what  part  had  he  left  ? 

31.  A  farmer,  having  160  bushels  of  wheat,  sold 
-i  of  |  of  it,  floured  f  of  |  of  it,  and  kept  the  re- 
mainder for  seed  ;  wrhat  part  of  the  whole  did  he  use 
for  each  purpose  ? 

32.  If  I  have  sold  f  of  f  of  120  sheep,  what  part 
of  the  whole  flock  have  I  left  ? 

33.  One  man  can  walk  4f  miles  while  another 
walks  3f  miles  ;  what  part  of  the  distance  that  the 
first  walks  does  the  second  walk  ? 

34.  A  gentleman  paid  |  of  $39|  for  a  coat,  and 
$9-|  for  a  pair  of  pantaloons  ;  how  many  times  as 
much  did  he  pay  for  the  coat  as  for  the  pantaloons  ? 

35.  Paid  $7f  for  a  barrel  of  flour,  and  1|  times 
as  much  for  a  ton  of  hay ;  what  was  the  cost  of  the 
liay  ? 

36.  A  man  bought  a  horse  for  $225,  and  a  car-f 
riage  for  ^  of  |  of  this  sum  ;  wrhat  part  of  $125  did' 
the  carriage  cost  ? 

37.  If  a  vessel  sail  40  miles  in  5  hours,  what  part 
of  144  miles  will  she  sail  in  9  hours  ?  how  many 
miles  ? 

38.  A  man  gave  to  his  3  sons  360  acres  of  western 
land  ;  to  the  first  he  gave  f  of  it,  to  the  second  |  of 
3|-  times  as  much,  and  the  remainder  he  gave  to  the 
third  ;  what  part  of  the  whole  did  each  receive  ?  how 
many  acres  ? 

39.  A  merchant  gained  on  a  hogshead  of  sugar 
f  of  f  46f ,  which  was  |  of  2  times  what  it  cost  him  ; 
what  did  it  cost  him  ?  what  part  of  the  cost  was  the 
gain  ? 


116  INTELLECTUAL   ARITHMETIC.  [75. 

75.  1.  If  G  cords  of  wood  cost  $15,  what  will 
4  cords  cost  ? 

ANALYSIS.     Four  cords  are   £,   or  §  of  6   cords.     Ij 

6  cords  of  wood  cost   $15,  4   cords  will   cost  §  of  $15  ; 
£  o/  $15   is   $5,  awrf  f  o/  $15   is   2  times    $5,  or  $10. 
Therefore,  fyc. 

Or,  Me  JM/M/  may  wse  the  form  of  analysis  used  in  section 
on  page  41. 

2.  If  9  pounds  of  sugar  cost  75  cents,  what  will 
12  pounds  cost '.' 

3.  If  6  men  can  cut  45  cords  of  wood  in  3  days, 
how  many  cords  can  8  men  cut  in  the  same  time  ? 

4.  If  3*  yards  of  cloth  cost  $10  J,  how  much  will 

7  yards  cost  ? 

5.  If  4|  pounds  of  butter  cost  GG  cents,  what  will 
2|  pounds  cost  ? 

6.  If  a  mechanic  earn  18J  shillings  in  1£  days, 
how  much  can  he  earn  in  a  week  ? 

7.  If  $7 1  will  buy  3-J  cords  of  wood,  how  many 
cords  can  be  bought  for  JlO-J  ? 

8.  If  £  barrel  of  flour  cost  $4 J,  what  will  f  of  a 
barrel  cost  ? 

ANALYSIS.  What  part  of  ±  is  f  ?  £  =  g,  and  f  •=.  f  ; 
Me  ra^'o  o/*  |  to  |-  is  the  same  as  of  3  to  4,  nz  |-.  7%£/?,  smee 
4  barrel  of  flour  cost  $4£,  §  q/*  a  barrel  will  cost  ^  of  $4£ ; 
|  o/  f  =  %6-  =  $6.  Therefore,  $c. 

9.  If  a  man  can  run  G  miles  in  ^  of  an  hour,  how 
far  can  he  run  in  3^  hours  ? 

10.  How  many  yards  of  carpeting  |  of  a  yard 
wide  are  equal  to  12  yards  f  of  a  yard  wide  ? 

11.  If  a  staff  3  feet  long  cast  a  shadow  5  feet  in 
length,  what  would  be  the  length  of  the  shadow  cast 
by  a  pole  13  feet  long  ? 

12.  If  the  sawing  of  f  of  a  cord  of  wood  cost  6J 
shillings,  what  would  the  sawing  of  3|  cords  cost  ?  " 


7t5.]  INTELLECTUAL   ARITHMETIC.  117 

13.  John  earns  9  cents  as  often  as  James  earns  15 
cents ;  when  John  has  earned  63  cents,  how  much 
has  James  earned  ? 

14.  Two  persons  start  from  different  points  and 
travel   towards  each  other ;  the   first   one  travels  7 
miles  while  the  other  travels  5  miles,  and  when  they 
meet  the  first  one  has  traveled  70  miles ;  how  far 
apart  were  they  when  they  started  ? 

15.  If  4  men  can  build  a  wall  60  feet  long  in  6 
days,  in  what  time  can  3  men  build  a  wall  90  feet  in 
length  ? 

ANALYSIS.  In  $  of  §-°-  of  6  days,  which  are  12  days. 
Or  thus  :  if  it  will  take  4  men  6  days  to  build  a  wall  60  feet 
long,  it  iv ill  take  1  man  4  times  6  days,  or  24  days,  and  3 
men  can  do  it  in  ±  of  24,  or  8  days  ;  to  build  a  wall  1  foot 
long  will  require  ^  of  8,  or  ^  days,  and  to  build  a  wall 
90  feet  long  will  require  90  times  as  many  days,  or  90  times 
e8g-,  equal  to  12  days.  Therefore,  8?c. 

16.  If  5  men  can  do  a  piece  of  work  in  10  days, 
how  many  men  will  do  a  piece  of  work  4  times  as 
large  in  20  days  ? 

17.  If   a  man  perform  a  journey  in  8  days,  by 
traveling  9  hours  a  day,  how  many  days  will  he  re- 
quire to  perform  the  same  journey,  if  he  travel  1  % 
hours  a  day  ? 

18.  If  5  horses  eat  1|-  tons  of  hay  in  1  month,  lio"W 
many  tons  will  6  horses  eat  in  2|-  months  ? 

19.  How  many  days  will  it  take  5  men  tc-  earn 
$11|,  if  3  men  earn  $f  in  \  of  a  day  ? 

20.  If  1  horse  eat  1^  bushels  of  oats  in  3  days,  in 
how  many  days  will  4  horses  eat  49  bushels  ? 

21.  If  a  barrel  of  flour  will  supply  a  family  of  4 
persons  5  weeks,  how  much  will  supply  a  family  of 
3  persons  2^  weeks  ? 

22.  If  3  "furnaces  consume  121  tons  Of  coal  in  7 
days,  how  long  will  1H  tons  last  5  furnaces  ? 


118  INTELLECTUAL  ARITHMETIC.  [76. 

76.  CHAPTER   VIII. 

PERCENTAGE. 

THE  term?,  percentage  and  per  cent., signify  by  the  hun- 
dred, or  hundredth*,  that  is,  a  certain  number  of  parts  of  each 
one  hundred  parts,  of  whatever  denomination.  Thus,  by  5 
per  cent,  is  meant  f)  cents  of  every  100  cents,  $5  of  every 
$100,  5  bushels  of  every  100  bushels,  &c.  Therefore,  5 
per  cent,  equals  5  hundredth?,  (T§ff,)  or  -2\s-  8  per  cent.,  8 
liundredths,  (T§o?)  °r  &  of  the  given  number  or  quantity. 

1.  A  man,  having  $40,  lost  3  per  cent,  of  it ;  how 
many  dollars  did  he  lose  ? 

ANALYSTS.  Since  he  lost  3  per  cent.,  or  T^,  on  $1, 
on  $40  he  lost  40  times  Tjfo,  or  fgg-  of  $1,  equal  to  $1-J. 
Therefore,  $c. 

2.  What  is    5  per  cent,  of  $25  ?  of  $30  ?  of   $45  ? 

3.  What  is    7  per  cent,  of  $15  ?  ol  $40  ?  of  $200  ? 

4.  What  is    6  per  cent,  of  $18  ?  of  $37  ?  of   $54  ? 

5.  What  is    3  per  cent,  of    50  bushels  of  corn  ? 
G.  What  is  10  per  cent,  of  160  tons  of  plaster  ? 

7.  What  is  25  per  cent,  of    96  gallons  of  wine  ? 

8.  What  is  12  per  cent,  of  33i  pounds  of  sugar  ? 
0.    What  is  15  per  cent,  of  110  barrels  of  flour  ? 

10.  What  is    8  per  cent,  of    28  yards  of  cloth  ? 

11.  What  is    f  per  cent,  of  $45  ? 

ANALYSIS.  Since  1  per  cent  of  $45  is  T40^-,  §  of  1  p*r 
cent,  is  §  of  TVu,  or  T3<&,  equal  to  $-&.  Therefore,  $c. 

12.  What  is    f  per  cent,  of  $28  ?  of  $44  ?  of  $56  ? 

13.  What  is    £  per  cent,  of  $63  ?  of  $120  ? 

14.  What  is    f  per  cent,  of  30  barrels  of  cider  ? 

15.  What  is  3J  per  cent  of  70  sheep  ?  of  35  cows  ? 

16.  What  is  2^  per  cent,  of  34  hundred  weight? 


77".]  INTELLECTUAL   ARITHMETIC.  119 

17.  A  man  bought  75  barrels  of  apples,  and  on 
opening  them,  found  8  per  cent,  of  them  spoiled ; 
how  many  barrels  did  he  lose  ? 

18.  If  I  have  $200  deposited  in  the  bank,  and 
draw  out  15  per  cent,  of  it,  how  much  remains  ? 

19.  A  farmer,  having  176  sheep,  sold  75  per  cent. 
»f  them,  and  kept  the  remainder ;  how  many  did  he 
keep? 

20.  A  young  man,  having  $104,  lost  12|-  per  cent, 
of  it  in  gambling ;  how  many  dollars  dicl  he  lose, 
and  what  per  cent,  of  the  whole  had  he  left  ? 


77.  1.  What  fraction  of  a  number  is  8  per  cent, 
of  it? 

ANALYSIS.  Since  1  per  cent,  is  T<jg-,  8  per  cent,  is  8 
times  T^,  or  T§JJ,  —  •/%•  Therefore  8  per  cent,  equals  •/$ 
of  any  number  or  thing. 

2.  What  fraction  of  a  number  is  6  per  cent.  ?  7 
per  cent.  ?  10  per  cent.  ?  12|-  per  cent.  ? 

3.  What  fraction  of  a  number  is  6-J-  per  cent.  ? 
16|  per  cent.  ?  20  per  cent.  ?  37|  per  cent.  ?  40  per 
cent.  ? 

4.  If  you  have  8120,  and  lose  33^  per  cent,  of  it, 
what  part  of  it  will  you  lose  ? 

5.  James,  having  250  marbles,  lost  40  per  cent,  of 
them  at  play ;  what  part  of  the  whole  had  he  left, 
and  how  many  did  he  lose  ? 

6.  What  per  cent,  of  a  barrel  of  flour  is  -f  of  it  ? 

ANALYSIS.  Since  the  whole  of  any  number  or  thing  is 
equal  to  100  per  cent.,  f  of  one  barrel  of  flour  is  equal  to 
f  of  100  per  cent.,  or  40  per  cent.  Therefore,  fye. 

7.  If  a  man  save  -|  of  his  income,  what  per  cent. 
does  he  spend  ? 

8.  If  a  merchant  invest  f  of  his  money  in  dry 
goods,  what  per  cent,  does  he  invest  ? 


120  INTELLECTUAL   ARITHMETIC.  [78. 

78.  1.  A  farmer,  having  20  sheep,  lost  5  of  them 
by  disease  ;  what  per  cent,  did  he  lose  ? 

ANALYSIS.  Since  20  sheep  are  100  per  cent.,  or  all  that 
he  had,  5  sheep  are  •£$,  or  £,  of  all  he  had ;  and  £  of  100 
per  cent,  is  25  per  cent.  Therefore,  fyc. 

2.  What  per  cent,  of  21  is  7  ? 

3.  What  per  cent,  of  50  is  5  ?  10  ?  20  ?  25  ? 

4.  What  per  cent,  of  $40  is  $5  ?  $8  ?  $25  ?  $30  ? 

5.  What  per  cent,  of  18  pounds  is  3  pounds  ?  12 
pounds  ? 

6.  What  per  cent,  of  42  miles  is  6  miles  ?  7  miles  ? 

7.  What  per  cent,  of  12*  is  2*-  ?  6-J  ? 

8.  What  per  cent,  of  30  is  12^?  15  ?  20  ? 

9.  What  per  cent,  of  18  is  9  ?  12  ?  15  ? 

10.  1J  is  what  per  cent,  of  9  ?  of  15  ?  of  21  ? 

11.  2|-  is  what  per  cent,  of  7£  ?  of  12*  ?  of  10  ? 

12.  -J  is  what  per  cent,  of  3j"?  of  16| "?  of  20  ? 

13.  *£  is  what  per  cent,  of  8  ?  of  12  ?  of  20  ? 

14.  If   from  a  hogshead  of  molasses  a  grocer  draw 
42  gallons,  what  per  cent,  of  the  whole  will  remain  ? 

15.  From  a  box  of  tea  containing  60  pounds,  15 
poimds  were  sold  at  one  time,  and  25  pounds  at 
another ;  what  per  cent,  of  the  wholo  remained  un- 
sold ? 

16.  In  a  heap  of  potatoes  containing  150  bushels, 
3  bushels  of  every  5  are  bad  ;  what  per  cent,  are 
bad,  and  how  many  bushels  are  good  ? 

17.  A  gambler,  having  $250,  lost  $80  at  play; 
what  per  cent,  of  his  money  did  he  lose,  and  what 
per  cent,  had  he  left  ? 

18.  James,  having  62£  cents,  gave  37-J-  for  a  book  ; 
what  per  cent,  of  his  money  had  he  left  ? 

19.  A  grocer,  having  a  barrel  of  sugar  containing 
200  pounds,  sold  ^  of  it  at  one  time,  and  ^  of  the 
remainder  at  another  time  ;  what  per  cent,  remained 
unsold  ? 


79.]  INTELLECTUAL   ARITHMETIC.  121 

79.  1.  A  person  collects  $240,  and  receives  £ 
per  cent,  commission  on  what  he  collects  ;  what  com> 
pensation  does  he  receive  ? 

ANALYSIS.  Since  the  commission  is  5  per  cent.,  or  y^^ 
equal  to  £$,  of  the  sum  collected,  he  receives  ^  of  $240, 
which  is  $12.  Therefore,  fyc. 

2.  What  will  be  the  expense  of  collecting  a  note 
of  $800,  at  10  per  cent,  commission  ? 

3.  What  must  be  paid  for  collecting  a  tax  of  $300, 
allowing  12|  per  cent,  commission  ? 

4.  An  agent  sells  $1200  worth  of  merchandise,  at 
25  per  cent,  commission ;  how  much  will  he  receive 
for  his  services  ? 

5.  An   auctioneer   sold  goods  to  the  amount  of 
$500  ;  what  will  his  commission  amount  to,  at  2^- 
per  cent.  ? 

6.  Paid  an  attorney  3|-  per  cent,  to  collect  a  debt 
of  $640  ;  how  much  did  he  receive  for  his  services  ? 

7.  If  a  man  fail  in  business,  and  can  pay  but  40 
per  cent,   of  his  debts,  how  much  will  a  creditor 
receive  on  a  debt  of  $175  ? 

8.  Bought  $1000  worth  of  books,  receiving  a  com- 
mission of  3|  per  cent. ;  how  much  did  I  receive  for 
my  services  ? 

9.  If  a  broker  sell  $600  worth  of  New  York  Cen- 
tral Railroad  stock,  and  charge  |  per  cent,  for  selL 
ing,  how  much  will  he  receive  ? 

10.  At  |  of  1  per  cent.,  what  will  be  the  expense 
of  negotiating  a  bill  of  exchange  of  $625  ? 

11.  A  broker  in  Chicago  exchanged  $1200  on  the 
Chemical  Bank  of  New  York,*  at  f  per  cent. ;  what 
amount  of  brokerage  did  he  receive  ? 

12.  A  real  estate  agent  sells  a  house  and  lot  for 
$2000,  and  charges  1J  per  cent,  commission  for  sell- 
ing ;  how  much  does  he  receive  ? 


122  INTELLECTUAL   ARITHMETIC.  [8O. 

8O.  1.  A  merchant  sends  his  agent  $780  to  ex- 
pend for  merchandise,  after  deducting  his  commis- 
sion of  4  per  cent. ;  what  sum  will  he  expend  ? 

ANALYSIS.  The  money  to  be  expended  is  -f gg  of  itself, 
and  the  commission  TJjj,  or  ^,  of  this  sum;  hence  the 
whole  amount  sent  to  the  agent  is  |JJ  $,  or  ff.  Since  $780 
*5  M'  2T  ^  2*5  °/  &78^  or  $^°>  ^  commission;  and  f  g-  /s 
25  feme*  30,  or  $750,  ^e  sz«/w  to  fo  expended. 

2.  I  gave  a  broker  $810  to  invest  in  bank  stock, 
after  deducting  his  commission  of  1|  per  cent.  ;  what 
was  his  commission,  and  how  much  did  he  invest  ? 

3.  A  distiller  sent  Mr.  B.  $1550,  with  which  to  buy 
corn,  after  deducting  his  commission  of  3^  per  cent. ; 
how  much  did  he  expend,  and  how  much   did  his 
commission  amount  to  ? 

4.  How  many  bushels  of  wheat,  at  $1  a  bushel, 
can  an  agent  buy  for  $1230,  and  retain  2|  per  cent, 
commission  for  his  trouble  ? 

5.  A  farmer  employed  a  man  to  thresh  his  wheat, 
agreeing  to  give  him  12  per  cent,  of  all  he  threshed ; 
how  many  bushels  must  he  thresh  that  the   farmer 
niay  retain  68  bushels? 

ANALYSIS.  Since  the  thresher  received  T\j2jy,  or  -/$  of  all 
he  threshed,  the  farmer  received  the  difference  between  -{%$, 
or  J|  and  2\,  which  is  f  f .  Then  66  bushels  is  f  §  of  the 
whole  number  of  bushels  threshed ;  since  66  bushels  is  §§, 
2*5  *5  sV  °f  66,  or  3  bushels,  and  f  |  is  25  times  3  bushels, 
or  75  bushels.  Therefore,  fyc. 

6.  What  amount  must  be  collected  on  a  rate  bill, 
that  the  collector  may  retain  his  fee  of  5  per  cent., 
and  pay  over  $228  ?  * 

7.  What  amount  of  accounts  must  an  individual 
collect  in  order  to  pay  over  $1100,  and  retain  8^  per 
cent,  for  collecting  ? 


81.]  INTELLECTUAL   ARITHMETIC.  123 

81.  1.  What  must  be  paid  for  insuring  a  house 
and  furniture  for  $1000,  at  1J  per  cent,  premium  V  * 

ANALYSIS.  Since  the  premium  is  1^  per  cent.,  or  ^^, 
equal  to  -£-ff  of  the  amount  insured,  the  premium  on  $1000 
will  be  Js  of  $1000,  or  $12£.  Therefore,  $c. 

2.  What  will  be  the  premium  for  insuring  200 
barrels  of  flour,  valued  at  $1200,  at  4  per  cent.  ? 

3.  What  must  I  pay  annually  for  an  insurance  of 
$900  upon  my  life,  at  2|  per  cent.  ? 

4.  What  must  be  paid  for  insuring  a  case  of  cloths, 
valued  at  $600,  at  1|  per  cent,  premium  ? 

5.  What  is  the  annual  premium  of  insurance,  at 
|  per  cent.,  011  a  building  valued  at  $4000  ? 

6.  If  a  merchant  has  his  stock  of  goods  insured 
for  $2500,  at  |  of  1  per  cent.,  what  is  the  premium  ? 

7.  A  man  owns  |  of  a  boat  load  of  grain,  valued 
at  $1600,  and  insures  his  interest  at  1|  per  cent ; 
what  premium  does  he  pay  ? 

8.  At  2  per  cent.,  what  amount  of  insurance  can 
I  obtain  for  $18  premium  ? 

ANALYSIS.  Since  2  per  cent,  premium  is  T§-<j,  or  ^  of 
the  amount  insured,  $18,  the  given  premium,  will  be  equal 
to  -i$  of  the  required  amount  of  insurance  ;  $18  is  -£$  (>f  50 
times  $18,  equal  to  $900.  Therefore,  $c. 

9.  At  3  per  cent.,  what  amount  of  insurance  can 
be  obtained  on  a  house  for  $75  ? 

10.  At  -|  per  cent.,  what  amount  of  insurance  can 
be  obtained  on  a  boat  load  of  flour,  for  $24  ? 

11.  What  amount  of  insurance  can  be  had  for 
$45,  upon  a  car  load  of  horses,  at  44-  per  cent.  ? 

12.  If  the  rate  is  If  per  cent.,  and  the  premium 
paid  is  $91,  what  will  be  the  amount  of  insurance 
obtained  on  a  store  and  its  contents  ? 

*  The  sum  paid  for  insurance  is  called  the  premium. 


124  INTELLECTUAL   ARITHMETIC. 

82.  1.  If  a  man  buy  a  horse  for  $90,  for  how 
much  must  he  sell  him  to  gain  20  per  cent.  ? 

ANALYSIS.  Since  he  gains  20  per  cent.,  or  -^0°(7,  equal  to 
\  of  what  the  horse  cost  him,  he  must  sell  him  for  &  of  what 
he  cost ;  £  of  S'JO  is  $18,  and  g-  <//'  $(JO  is  6  tofeg  $18,  or 
$108.  Therefore,  $c. 

2.  A  sleigh  was  bought  for  $f;0,  and  sold  for  8  per 
cent,  more  than  it  cost  ;  what  was  it  sold  for  ? 

3.  Bought  a  quantity  of  sugar  for  $84,  and  sold  it 
at  an  advance  of  12£  per  cent ;  what  was  it  sold  for? 

4.  A  grocer  bought  some  tea  for  $45,  but  finding 
it  damaged,  lie  was  obliged  to  sell  it  at  a  loss  of  10 
per  cent.  ;  what  did  he  sell  it  for  ? 

•5.  Paid  -SI 2  for  15  yards  of  cloth;  what  must  it 
be  sold  for  a  yard  to  gain  25  per  cent.  ? 

G.  A  drover  bought  60  sheep  for  $180,  and  sold 
them  at  a  loss  of  20  per  cent,  on  the  cost ;  what 
did  he  receive  per  head  for  them  ? 

7.  A  grocer  bought  440  lemons  for  $12,  and  after 
throwing  away  10  per  cent,  of  them,  lacking  4,  as 
worthless,  he   sold  the  remainder  so  as  to  gain  88A 
per  cent,  on  the  cost  of  the  whole ;  what  did  he  sell 
them  for  apiece  ? 

8.  Bought  6  barrels  of  flour  for  $40 ;  for  what 
must  it  be  sold  a  barrel  to  gain  5  per  cent,  on  the 
cost  ? 

9.  If  I  buy  eggs  at  10  cents  a  dozen,  how  must 
I  sell  them  to  gain  30  per  cent.  ? 

10.  A  speculator  bought  a  quantity  of  pork  for 
$500,  and  sold  it  at  a  loss  of  7  per  cent. ;  with  the 
proceeds  he  bought  another  quantity,  upon  which  he 
gained  20  per  cent. ;  what  was  his  gain  on  the  whole  ? 

11.  Bought  hay  at  $14  dollars  a  ton,  which  was 
12|  per  cent,  less  than  the  market  price  ;  what  was 
the  market  price  ? 


83.]  INTELLECTUAL   ARITHMETIC.  125 

83.  1.  What  is  gained  per  cent,  by  selling  clover 
seed  for  $6,  that  cost  $4  ? 

ANALYSIS.  The  whole  gain  is  equal  to  the  difference 
between  $6  and  $4,  which  is  $2.  Since  $4  gain  $2,  or  £ 
of  itself,  equal  to  f^,  the  gain  will  be  50  per  cent.  There- 
fore, fyc. 

2.  What  per  cent,  is  gained  by  selling  pork  for 
$7  a  hundred  weight,  that  cost  $6  ? 

3.  What  will  be  gained  by  expending  $500  for 
sugar,  when  it  can  be  bought  for  8  cents,  and  sold 
for  8|-  cents  a  pound  ? 

4.  "if  I  buy  $300  worth  of  sheep,  and  sell  them 
for  $375,  what  do  I  gain  per  cent.  ? 

5.  Mr.  C.  bought  a  horse  for  $153,  and  sold  him 
for  $128  ;  what  per  cent,  did  he  lose  ? 

6.  A  grocer  bought  eggs  for  9  cents  a  dozen,  and 
sold  them  for  12  cents  ;  what  per  cent,  did  he  gain  ? 

7.  What  per  cent,  is  lost  in  buying  corn  at  50 
cents  a  bushel,  and  selling  it  at  45  cents  ? 

8.  If  a  house  bring  J  of  its  value  every  4  years  in 
rent,  what  is  the  gain  per  cent,  each  year  ? 

9.  Bought  a  horse  for  20  per  cent,  less  than  $150, 
and  sold  him  for  10  per  cent  more  than  $150  ;  what 
per  cent,  was  gained  ? 

10.  A  peddler  bought  oranges  for  18  cents  a  dozen, 
and  sold  them  for  2  cents  each  ;  what  per  cent,  did 
he  gain  ? 

11.  A  farmer  refused   to  sell  his  barley  for  75 
cents  a  bushel,  and  was  afterwards  obliged  to  take 
60  cents  a  bushel  for  it ;  what  per  cent,  did  he  lose  ? 

12.  Bought  cotton  cloth  at  1±  cents  a  yard,  and 
sold  it  for  9  cents  a  yard  ;  what  was  the  gain  per 
cent.  ? 

13.  Sold  damaged  cloth  so  as  to  lose  J  of  what  it 
cost ;  what  per  cent,  was  lost  ? 


126  INTELLECTUAL   ARITHMETIC.  [84. 

84.  1.  A  tailor  sold  a  coat  for  $24,  by  which  he 
gained  20  per  cent,  on  the  first  cost  ;  what  was  its 
cost? 

ANALYSIS.  Since  he  gained  20  per  cent.,  or  -J  of  the 
cost,  $24  is  f  of  the  cost  ;  since  $24  is  f  ,  £  of  $24,  or  $4, 
is  $  °f  the  cost,  and  $4  is  |  of  5  times  $4,  or  $20.  There- 
fore, $c. 


2.  A  hatter  sold  a  hat  for  $3£,  which  was 
per  cent,  above  cost  ;  what  did  it  cost  ? 

3.  A  jeweler  sold  a  watch  for  $65,  thereby  gain- 
ing 30  per  cent,  on  its  cost  ;  what  was  its  cost  ? 

4.  A  mechanic  sold  a  carriage  for  $108,  which 
was  10  per  cent,  less  than  it  cost  ;  how  much  would 
he  have  received  for  it  had  he  sold  it  so  as  to  gain 
20  per  cent.  ? 

5.  If  16|  per  cent,  is  gained  by  selling  flour  at 
$7  a  barrel,  what  did  it  cost  ? 

6.  A  merchant  hold  2  barrels  of  sugar  for  $24 
each  ;  on  one  barrel  he  gained  20  per  cent,   and  on 
the  other  he  lost  20  per  cent.  ;  did  he  gain  or  lose 
by  the  bargain,  and  how  much  ? 

7.  A  grocer  bought  coffee  so  that  he  could  sell  it 
for  18  cents  a  pound,  and  make  a  profit  of  33  J  per 
cent.  ;  what  did  it  cost  him  ? 

8.  A  man  bought  a  horse  and   carriage  ;  he  sold 
them  both  at  8  per  cent,  above  cost,  receiving  $81 
for  the  horse,  and  $108  for  the  carriage  ;  what  was 
the  cost  of  both  ? 

9.  A  fruit  dealer  sold  pine-apples  at  96  cents  a 
dozen,  thereby  losing  4  per  cent.  ;  what  did  they  cost 
apiece  ? 

10.  B  sells  a  horse  to  C,  and  gains  12  J  per  cent.  ; 
C  sells  him  to  D  for  $118,  and  thereby  gains  18  per 
cent.  ;  how  much  did  the  horse  cost  B  ? 


85.]  INTELLECTUAL   ARITHMETIC.  121 

85.  1.  Sold  wheat  so  as  to  gain  16  cents  on  fv 
bushel,  which  was  12  J  per  cent,  of  what  ?+,  cost ;  what 
did  it  cost  ? 

2.  A  broker  exchanged  $150  at  J  per  cent.  ;  how 
much  brokerage  did  he  receive  ? 

3.  A  man,  having  a  farm  of  200  acres,  sold  75 
acres  of  it ;   what  per  cent,  of  the  whole  remains 
unsold  ? 

4.  What  per  cent,  does  William  gain  by  selling 
apples  at  -|  of  the  cost  ? 

5.  If  I  buy  stoves  at  $12  each,  and  sell  them  at 
8J  per  cent,  profit,  what  will  I  gain  on  1  stove  ? 

6.  If  a  broker  buy  $800  worth  of  bank  stock  for 
me,  and  charge   ^  per  cent,  brokerage,  how  much 
will  he  receive  ? 

7.  Sold  butter  so  as  to  gain  |-  as  much  as  it  cost ; 
what  per  cent,  was  gained  ? 

8.  Mr.  A.  lends  his  money  so  as  to  receive  a  sum 
equal  to  •£§  of  it  for  its  use ;  what  per  cent,  does  he 
receive  ? 

9.  A  brewer  sends  a  person  $520  with  which  to 
purchase  barley,  after  deducting  his  commission  of  4 
per  cent. ;  how  much  does  he  expend,  and  how  much 
does  his  commission  amount  to  ? 

10.  The  cost  of  building  a  town  house,  and  paying- 
collector's  fees  of  5  per  cent.,  was  $945  ;  what  was  the 
cost  of  the  house  ? 

11.  Hiram  agrees  to  dig  farmer  F.'s  potatoes  for 
8  per  cent,  of  what  should  be  put  into  the  farmer^ 
cellar ;    he   digs   324   bushels  ;    how  many  bushels 
should  be  put  into  the  cellar,  and  how  many  bushels 
should  Hiram  receive  ? 

12.  Bought  $200  worth  of  dry  goods,  and  $300 
worth  of  groceries  ;  on  the  dry  goods  I  lost  20  per 
cent.,  but  on  the  groceries  I  gained  15  per  cent. ;  did 
I  gain  or  lose  on  my  whole  capital,  and  how  much  ? 


128  INTELLECTUAL   ARITHMETIC.  [S3. 

13.  A  merchant  bought  40  bushels  of  grass  seed, 
at  the  rate  of  4  bushels  for  $ 6,  and  sold  it  at  the 
rate  of  5  bushels  for  $8 ;  what  was  his  whole  gain, 
and  what  his  gain  per  cent.  ? 

14.  A  drover  bought  20  sheep  for  $50,  and  sold 
them  so  as  to  gain  20  per  cent. ;  how  much  did  he 
receive  a  head  for  them  ? 

15.  A  man  bought  60  cords  of  wood  for  $200, 
and  sold  it  at  a  loss  of  5  per  cent. ;  at  what  price 
did  he  sell  it  per  cord  '.' 

16.  If  I  buy  rice  at  4  cents  a  pound,  and  sell  it 
at  5  cents,  what  is  my  gain  per  cent.  ? 

17.  Sold  a  cow  at  auction  for  $18  that  cost  $20  ; 
what  was  the  loss  per  cent.  ? 

18.  A  boy  bought  peaches  at  the  rate  of  3  for  2 
cents,  and  sold  them  at  the  rate  of  9  for  7  cents; 
what  was  his  gain  per  cent.  ? 

19.  A  tailor  sold  two  coats  for  $26  each ;  on  one 
he  gained  30  per  cent.,  and  on   the  other  he  lost 
80  per  cent.;  did  he. gain  or  lose  on  both,  and  how 
much  ? 

20.  A  music  dealer  sold  a  piano-forte  for  $230, 
which  was  8  per  cent,  less  than  its  value ;  had  he 
<?old  it  for  $300,  what  would  have  been  his  gain  per 
uent.  ? 

21.  Two  men  buy  a  lot  of  pork  together  ;  A  fur- 
nishes $200,  and  B  $150 ;  their  profits  are  $70 ;  what 
is  their  gain  per  cent.,  and  what  is  each  one's  share 
of  the  gain  ? 

22.  If  a  ton  of  hay  is  bought  for  -f  of  the  market 
price,  and  sold  for  5  per  cent,  more  than  the  market 
price,  what  per  cent,  is  gained  ? 

23.  A  person  engaged  in  speculation  sold  out  his 
interest  for  $2100,  which  was  30  per  cent,  less  than 
twice  as  much  money  as  he  began  with ;  how  much 
did  he  begin  with,  and  what  was  his  gain? 


86.]  f    INTELLECTUAL  ARITHMETIC.  129 

86.  INTEREST  is  a  sum  paid  for  the  use  of  borrowed 
money,  or  on  demands  after  they  become  due. 

The  PRINCIPAL  is  the  money  lent,  or  the  sum  for  which 
interest  is  paid. 

The  AMOUNT  is  the  sum  of  the  principal  and  interest. 

The  RATE  PER  CENT,  is  the  sum  paid  for  the  use  of 
$100  or  100  cents  for  one  year.  Thus,  if  $6  be  paid  for 
the  use  of  $100  one  year,  the  rate  is  6  per  cent,  per 
annum. 

The  interest  on  any  sum  for  one  year  is  always  a  certain 
number  of  hundredths  of  the  principal.  Thus,  the  interest 
of  any  sum  for  one  year,  at  5  per  cent.,  is  5  hundredths 
Ortfo)  or  2\r  of  the  principal ;  at  8  per  cent,  it  is  8  hun- 
dredths (T|hj)  or  ITS  °f  tne  principal. 

Practically,  30  days  are  considered  a  month,  and  12 
months  a  year,  in  computing  interest.  When  no  time  is 
named,  one  year  is  always  understood. 

The  rate  of  interest  is  established  by  law;  and  taking 
more  than  such  rates  is  termed  usury. 

1.  What  is  the  yearly  interest  of  880,  at  5  per  cent.  ? 

ANALYSIS.  Since  the  interest  is  5  per  cent.,  or  y^,  equal 
~*°  5TT  °f  th&  principal,  the  interest  of  $80  is  ^V  of  $80, 
or  $4.  Therefore,  $c. 

Or  thus  :  Since  the  interest  of  $1,  or  100  cents,  is  5  cents 
for  one  year,  the  interest  of  $80  is  80  times  5  cents,  or  400 
cents,  equal  to  $4.* 

2.  What  is  the  yearly  interest  of  $200,  at  6  per 
cent.  ? 

3.  What  is  the  yearly  interest  of  $125,  at  4  per 
cent.  ? 

4.  What  is  the  annual  interest  of  $60,  at  7  per 
cent.  ? 

5.  What  is  the  annual  interest  of  $95,  at  5  per 
cent.  ? 

*  The  fractional  method  is  considered  preferable  in  mental  exercises. 
9 


130  INTELLECTUAL   ARITHMETIC.     '  [87. 

6.  What  is  the  animal  interest  of  $26,  at  10  per 
cent.  ? 

7.  What  is  the  annual  interest  of  8228,  at 
per  cent.  ? 

8.  What  is  the  annual  interest  of  $96.32,  at  6£ 
per  cent.  ? 

9.  What  is  the  annual  interest  of  $144.60,  at  8£ 
per  cent.  ? 

10.  What  is  the  annual  interest  of  $400,  at  15 
per  cent.  ? 

11.  What  is  the  annual  interest  of  $500,  at  7 
per  cent.  ? 

12.  What  is  the  annual  interest  of  $120.80,  at  7£ 
per  cent.  ? 

13.  What  is  the  annual  interest  of  $1000,  at  9 
per  cent.  ? 

14.  What  is  the  annual  interest  of  $150,  at  3  per 
cent.  ? 


87.  1.  What  is  the  interest  of  $150  for  3  years, 
at  8  per  cent.  ? 

ANALYSIS.  Since  the  interest  for  1  year  at  8  per  cent, 
is  Tf  tf,  equal  to  /$,  of  the  principal,  for  3  years  it  is  3 
times  /-%,  or  ^,  of  the  principal.  ^  of  $150  is  $6,  and 
2\  of  $150  is  6  times  $6,  or  $36.  Therefore,  fyc. 

Or  thus  :  Since  the  interest  of  $150  for  1  year  at  8  per 
cent,  is  $12,  (86,)  for  3  years  it  is  3  times  $12,  or  $36. 

2.  What  is  the  interest  of  f  30  for  2  years,  at  5 
per  cent.  ? 

3.  What  is  the  interest  of  $50  for  4  years,  at  6 
per  cent.  ? 

4.  What  is  the  interest  of  $90  for  5  years,  at  7 
per  cent.  ? 

5.  What  is  the  interest  of  $75  for  3  years,  at  12 
per  cent.  ? 


88.]  INTELLECTUAL   ARITHMETIC.  131 

6.  What  is  the  interest  of  $64.96  for  2  years,  at 
6J  per  cent.  ? 

7.  A's  note  of  $25  has  been  due  2  years ;  what  is 
the  interest,  at  6  per  cent.  ? 

8.  Borrowed  $300   for   3   years,  at  7  per  cent, ; 
what  will  be  the  interest  ? 

9.  What  is  the  interest  on  a  note  of  $46.50,  for  5 
years,  at  10  per  cent.  ? 

10.  I  owe  two  notes,  one  for  $145,  due  in  2  years, 
at  5  per  cent.,  and  the  other  for  $200,  due  in  3  years, 
at  6  per  cent. ;  what  will  be  the  sum  of  the  interest 
that  I  must  pay  ? 

11.  What  is  the  interest  of  $225  for  2  years,  at  7 
per  cent.  ? 

12.  What  is  the  interest  of  $50  for  8  years,  at  6 
per  cent.  ? 

13.  What  is  the  interest  of  $400  for  2  years,  at 
5|  per  cent.  ? 

"14.    Gave  a  note  for  $88.96,  due  in  3  years,  at  6| 
per  cent ;  what  will  be  the  interest  ? 

15.  Gave  a  note  due  at  date,  for  $45.50,  but  did 
not  pay  it  until  the  end  of  5  years ;  what  was  the 
interest  due,  at  8  per  cent.  ? 


88.  1.  At  8  per  cent.,  what  part  of  $1  equals 
the  use  of  it  for  3  years  9  months  ? 

ANALYSIS.  Since  there  are  12  months  in  1  year,  9 
months  is  T95,  or  £  of  1  year,  and  3  years  9  months  are  equal 
to  3f,  or  i-f- years.  Since  the  interest  of  $1  for  1  year  at 

8  per  cent,  is  yg^,  equnl  to  •/%  of  the  principal,  for  3  years 

9  months,  it  is   3$   times,  or  Ig.,  of  ^,  equal  to  -fa  of  the 
principal,  or  $T3I7.      Therefore,  $c. 


2.   At  6  per  cent.,  what  part  of  $1  equals  the  use 
of  it  for  2  years  8  months  ? 


132  INTELLECTUAL   ARITHMETIC.  [88. 

3.  At  5  per  cent.,  what  part  of  any  sum  equals 
the  use  of  it  for  2  years  6  months  ? 

4.  At  7  per  cent.,  what  part  of  any  sum  equals 
the  interest  of  it  for  1  year  8  months  ? 

5.  What  part  of  any  sum  equals  the  interest  of  it 
for  3  years  2  months,  at  4  per  c<int. '.' 

6.  What  part  of  any  sum  equals  the  interest  of  it 
for  5  years  4  months,  at  9  per  cent.  ? 

7.  At  6J  per  cent.,  for  3  years  4  months,  what 
part  of  the  principal  equals  the  interest  ? 

8.  At  8  per  cent.,  for  5  years  5  months,  what  part 
of  the  principal  equals  the  interest  ? 

9.  At  7i  per  cent.,  for  2  years  11  months,  what 
part  of  the  principal  equals  the  interest  ? 

10.  At  6  per  cent.,  for  2  years  1  month,  what  part 
of  the  principal  equals  the  interest  ? 

11.  At  10  per  cent.,  for  4  years  10  months,  what 
part  of  the  principal  equals  the  interest  ? 

12.  At  8  per  cent.,  for  3  years  3  months  and  18 
days,  what  part  of  the  principal  equals  the  interest  ? 

ANALYSIS.  Since  30  days  make  a  month,  18  days  are 
.18.^  or  §  of  a  month  ;  and  since  12  months  make  a  year, 
I  month  is  TV  of  a  year ;  £  of  1  month  is  -i-  of  r^, 
or  ^  of  I  year,  and  3f  months,  equal  to  -*•£-,  is  18  times  -^, 
or  ^  of  a  year.  Hence  the  interest  of  $l/or  3T3^,  or  f.g 
years,  at  8  per  cent.,  is  T^\  of  it.  (885  Ex.  1.)  There- 
fore, fyc. 

13.  What  part  of  the  principal  equals  the  inter- 
est, for  2  years  5  months  and  10  days,  at  6  per  cent.  ? 

14.  What  part  of  the  principal  equals  the  interest, 
for  1  year  8  months  and  25  days,  at  7  per  cent.  ? 

15.  What  part  of  the  principal  equals  the  interest, 
for  2  years  3  months  and  6  days,  at  6  per  cent.  ? 

16.  What  part  of  the  principal  equals  the  interest, 
for  2  years  11  months  and  6  days,  at  5  per  cent.  ? 


89.]  INTELLECTUAL   ARITHMETIC.  133 

17.  At  7£  per  cent.,  for  8  months  10  days,  what 
part  of  the  principal  will  equal  the  interest  ? 

18.  At  6  per  cent.,  for  5  years  7  months  and  15 
days,   what   part   of    the   principal   will   equal   the 
interest  ? 

19.  At  8-J-  per  cent.,  for  3  years  5  months  and 
12  days,  what  part  of  the  principal  equals  the  in- 
terest ? 

20.  At  7  per  cent,,  for  11  months  3  days,  what 
part  of  the  principal  will  equal  the  interest  ? 

21.  At  4  per  cent.,  for  8  years  6  months  and  15 
days,  what  part  of  the  principal  will  equal  the  in- 
terest ? 


89.  1.  What  is  the  interest  of  $40  for  3  years 
4  months,  at  6  per  cent.  ? 

ANALYSIS.  3  years  4  months  equals  3£,  or  *g-  years; 
and  the  interest  of  any  sum  for  *g-  years,  at  6  per  cent., 
equals  %  of  it.  (88.)  |  of  $40  is  $8,  the  required  in- 
terest.  Therefore,  fyc. 

Or  thus :  Since  the  interest  of  $1  for  1  year,  at  6  per 
cent.,  is  6  cents,  for  $40  it  is  40  times  6  cents,  or  $2.40,  and 
for  3£  years  it  is  3  J  times  $2.40,  equal  to  $8. 

2.  What  is  the  interest  of  $150  for  2  years  10 
months,  at  8  per  cent.  ? 

3.  What  is  the  interest  of  $80.40  for  4  years  2 
months,  at  7  per  cent.  ? 

4.  What   is   the  interest   of  $240    for  1  year  9 
months,  at  5  per  cent.  ? 

5.  What  is  the  interest  of   $120    for  5  years  8 
months,  at  7-|-  per  cent.  ? 

6.  What  is  the  interest  of  $90     for   4  years  7 
months,  at  4  per  cent.  ? 

7.  What  is  the  interest  of  $500  for  10  months,  at 
6  per  cent.  ? 


134  INTELLECTUAL   ARITHMETIC.  [89. 

8.  What  is  the  interest  of  $128   for   2  years   9 
months,  at  6^  per  cent.  ? 

9.  What  is   the  interest   of  $125  for  1  year  4 
months,  at  7  per  cent.  ? 

10.  What  is  the  interest  of  $300  for  8  months,  at 
6  per  cent.  ? 

11.  What  is   the  interest  of  $50  for  5  years  7 
months  and  15  days,  at  8  per  cent.  ? 

ANALYSIS.     The  interest  of  any  sum  for  5  years  7  months 
and  15  days,  at  8  per  cent.,  equals  29o  of  **>  (88?  Ex.  12  ;) 
of  $50  is  $2£,  and  ^  of  $50  is  9  times  $2£,  equal  to 
Therefore,  $c. 


12.  What  is  the  interest  of  $75.60  for  4  years  5 
months  and  10  days,  at  9  per  cent.  ? 

13.  What  is  the  interest  of  $50  for  6  years  4 
months  and  24  days,  at  5  per  cent.  ? 

14.  What  is  the  interest  of  $300  for  4  years  7 
months  and  15  days,  at  8  per  cent.  ? 

15.  What  is  the  interest  of  $288  for  8  months  10 
days,  at  7£-  per  cent.  ? 

16.  What  is  the  interest  of  $1200  for  20  days,  at 
6  per  cent.  ? 

17.  What  is  the  interest  of  $40  for  9  months  5 
days,  at  4^-  per  cent.  ? 

18.  What  is  the  interest  of  $36.72  for  5  years  6 
months  and  20  days,  at  7  per  cent.  ? 

19.  What  is  the  interest  of  $120  for  2  years  1 
month  and  6  days,  at  12  J  per  cent.  ? 

20.  What  is  the  interest  of  $24  for  11  months  and 
20  days,  at  15  per  cent.  ? 

21.  What  is  the  interest  of  $2000  for  18  days,  at 
5  per  cent.  ? 

22.  What  is  the  interest  of  $1500  for  2  months 
and  24  days,  at  6  per  cent.  ? 


9Oo]  INTELLECTUAL   AEITHMETIC.  135 

90.  1.  What  will  be  the  amount  of  $60  for  2 
years  6  months,  at  6  per  cent.  ? 

ANALYSIS.  Since  the  interest  is  equal  to  •£$  of  the  prin- 
cipal, (885)  and  the  amount  is  equal  to  the  principal  and 
interest,  it  follows  that  f  g-,  the  principal,  added  to  -£$,  the 
interest,  equals  f  §,  the  amount.  -^  of  $60  is  $3,  and  f  $ 
of  $60  is  23  times  $3,  or  $69,  the  amount.  Therefore,  fyc. 

NOTE,    "When  more   convenient,  the  interest  may  first  be  found,  to 
which  add  the  principal,  and  the  result  will  be  the  amount. 

2.  What  is   the   amount   of   $36  for  4  years  2 
months,  at  7  per  cent.  ? 

3.  What  will   $120   amount   to   in   2   years   11 
months,  at  8  per  cent.  ? 

4.  What  will    $96.48    amount  to  in  3   years  4 
months,  at  6^  per  cent.  ? 

5.  What  will  $80.50   amount  to  in   6   years   8 
months,  at  4-J-  per  cent.  ? 

6.  What  will  $20.25  amount  to  in  12  years,  at  5 
per  cent.  ? 

7.  What  will  $1500  amount  to  in  10  months,  at 
10  per  cent.  ? 

8.  What  will  $150  amount  to  in  6  months  and  20 
days,  at  6  per  cent.  ? 

9.  What  will  $250  amount  to  in  9  months  and  18 
days,  at  7 J  per  cent.  ? 

10.  What  is  the  amount  of  $480  for  1  year  10 
months  and  25  days,  at  5  per  cent.  ? 

11.  What  is  the  amount  of  $500  for  3  years  4 
months  and  24  days,  at  6  per  cent.  ? 

12.  What  is  the  amount  of  $240  for  2  years  7 
months  and  6  days,  at  7  per  cent.  ? 

13.  What  is  the  amount  of  $1000  for  5  years  1 
month  and  6  days,  at  4  per  cent.  ? 

14.  What  is  the  amount  of  $120  for  10  years  6 
months  and  20  days,  at  3  per  cent,  ? 


136  INTELLECTUAL   ARITHMETIC.  [91. 

91.  1.  What  principal  in  3  years  9  months,  at 
8  per  cent.,  will  give  $90  interest  ? 

ANALYSIS.  Since  the  interest  for  3  years  9  months,  at  8 
per  cent.,  is  ^  of  the  principal,  (88,  j  $90  must  be  -fa  of 
the  required  principal  Since  $90  is  TV  yV  is  $  of  $90,  or 
$30,  and  $30  is  -^  of  10  times  $30,  or  $300,  the  principal. 
Therefore,  $c. 

2.  What  principal,  in  1  year  8  months,  at  9  per 
cent.,  will  give  $8t>  interest? 

3.  What  principal  in  11  months,  at  6  per  cent., 
will  give  $22  interest  ? 

4.  What  principal  in  7  months  15  days,  at  8  per 
cent.,  will  give  $40  interest? 

5.  A  rents  a  store  to  B  for  the  yearly  rent  of  $300, 
which  is  12  per  cent,  of  its  cost ;  what  did  it  cost  ? 

6.  A  gentleman  bought  6  horses,  for  which  he  paid 
a  sum  of  money  which  in  2  years  6  months,  at  4  per 
cent.,  would  have  given  him  $90  interest;  what  did 
he  pay  apiece  for  the  horses  ? 

7.  A  person  deposits  |  of  his  money  in  the  bank, 
which  brings  him  an  animal  income  of  $1500,  at  10 
per  cent. ;  the  remaining  |  he  invests  in  business 
which  yields  him  20  per  cent,  profit ;  what  are  his 
entire  capital  and  his  yearly  income  ? 

8.  Two  persons  engaged  in  trade  ;  A  furnished  4 
of  the  capital,  and  B  f ;  at  the  end  of  3  years  and  4 
months  they  found  that  they  had  made  a  clear  profit 
of  $5000,  which  is  121  per  cent,  per  annum  on  the 
money  invested  ;  how  much  capital  did  each  furnish  ? 

9.  A  capitalist  invested  -f  of  his  money  in  railroad 
stock,  which  depreciated  5  per  cent,  in  value ;  the 
remaining  -f  he  invested  in  bank  stock,  which  at  the 
end  of  1  year  had  gained  $1200,  which  was  12  per 
cent,  of  the  investment ;  what  was  the  whole  amount 
of  his  capital,  and  what  was  his  entire  loss  or  gain  ? 


92.]  INTELLECTUAL   ARITHMETIC.  137 

92.  1.  What  principal  will,  in  3  years  4  months, 
at  5  per  cent,  amount  to  $700. 

ANALYSIS.  Since  the  interest  for  3  years  4  months,  at  5 
per  cent,  is  ^  of  the  principal,  (88,)  the  principal  |,  added 
to  the  interest  £,  equals  the  amount  % ;  hence  $700  is  %  of 
the  principal  Since  $700  is  £,  %  is  |  of  $700,  or  $100, 
and  $100  w  £  o/  6  times  $100,  or  $600.  *  Therefore,  $c. 

2.  What  principal  in  5  years,  at  6  per  cent.,  will 
amount  to  $1300  ? 

3.  What  principal  in  1  year  6  months,  at  8  per 
cent.,  will  amount  to  $280  ? 

4.  What  principal  in  4  years  2  months,  at  3  per 
cent.,  will  amount  to  $630  ? 

5.  What  principal  in  10  years,  at  7  per  cent.,  will 
amount  to  $340  ? 

6.  What  principal  in  9  months,  at  10  per  cent., 
will  amount  to  $172  ? 

7.  What  principal. in  18  months,  at  4  per  cent., 
will  amount  to  $530  ? 

8.  The  amount  due  on  a  bond  and  mortgage  is 
$2900,  it  having  been  on  interest  7  years   6  months, 
at  6  per  cent.  ;  what  was  the  principal  ? 

9.  Two  men  bought  200  acres  of  land,  and  at  the 
end  of  2  years  sold  it  for  $1500,  which  was  an  ad- 
vance of  12|-  per  cent,  per  annum  on  its  cost ;  what 
did  it  cost  an  acre  ? 

10.  A  man  invested  f  of  all  he  was  worth  in  the 
lumber  trade,  and  at  the  end  of  2  years   8  months 
sold  out  his  entire  interest  for  $3100,  which  was  a 
yearly  gain  of  9  per  cent,  on  the  money  invested  ;  how 
much  was  he  worth  when  he  commenced  trade  ? 

11.  A's  money  is  to  B's  as  2  to  3 ;  if  £  of  A's 
money  be  put  at  interest  for  3  years  9  months,  at 
10  per  cent.,  it  will  amount  to  $550  ;    how   much 
money  has  each  ? 


138  INTELLECTUAL   ARITHMETIC.  [93. 

93.     1.   In  what  time,  at  5  per  cent.,  will  $60 

gain  $15  interest  ? 

ANALYSIS.  The  gain,  or  interest,  is  ££,  or  %  of  the  prin- 
cipal, equal  to  25  per  cent,  of  the  principal.  (77?  Ex.  7.) 
Jf  a  given  principal  gain  5  per  cent,  in  1  year,  it  will  re- 
quire as  many  years  to  gain  25  per  cent,  as  5  per  cent,  is 
contained  times  in  25  per  cent.,  or  5  years.  Therefore,  §c. 

Or  thus :  Since  $60  in  1  year,  at  5  per  cent.,  will  gain 
$3  interest,  it  will  require  as  many  years  for  $GO  to  gain 
$15  interest,  as  $3  is  contained  times  in  $15,  which  is  5 
times. 

2.  How  long  will  it  take  $120  to  gain  $24  interest, 
at  6  per  cent.  ? 

3.  In    what  time  will  $500  gain  $35,  at  7  per 
cent.  ? 

4.  In  what  time  will  $120  gain  $40,  at  10  pe* 
cent.  ? 

5.  In  what  time  will  $80  gain  $6,  at  3  per  cent.  ? 

6.  In  what  time  will  $300  gain  $84,  at  7  per 
cent,  ? 

7.  In  what  time  will  $160  gain  $20,  at  6£  per 
cent.  ? 

8.  In  what  time  will  $49  gain  $12.25,  at  5  per 
cent.  ? 

9.  In  what  time  will  any  given  principal  double 
itself  at  4  per  cent.  ? 

ANALYSIS.  Since,  to  double  itself,  any  sum  of  money 
must  gain  100  per  cent.,  at  1  per  cent.,  it  will  require  100 
years,  at  4  per  cent.,  ^  of  100  years,  or  25  years.  There- 
fore, fyc. 

10.  In  what  time  will  a  given  principal  double  it- 
self at  5  per  cent.  ? 

11.  In  what  time  will  a  given  principal  double  it- 
self at  7  per  cent,  ? 


94.]  INTELLECTUAL   ARITHMETIC.  139 

12.  In  what  time  will  a  given  principal  double  it- 
self at  6  per  cent.  ? 

13.  In  what  time  will  a  given  principal  double  it- 
self at  10  per  cent.  ? 

14.  -In  what  time  will  $500  double  itself,  at  12J 
per  cent.  ? 

15.  In  what  time  will  $175  double  itself  at  20  per 
cent.  ? 

16.  In  what  time  will  a  given  principal  treble  it- 
self at  5  per  cent.  ? 

ANALYSIS.  A  given  principal  will  treble  itself  at  1  per 
cent,  in  200  years  ;  at  5  per  cent,  in  \  of  200  years,  or  40 
years. 

17.*  In  what  time  will  $100  treble  itself  at  6  per 
cent.  ?  at  7  per  cent.  ?  at  8  per  cent.  ?  at  10  per 
cent.  ? 


94.  1.  A  man  loaned  $75  for  4  years,  and  re- 
ceived $18  interest ;  what  was  the  rate  per  cent.  ? 

ANALYSIS.  Since  the  gain,  or  interest,  for  4  years,  is 
£|,  or  -/-$  of  the  principal,  for  1  year  it  is  J-  of  -£$,  or  T{fo 
of  the  principal,  equal  to  G  per  cent.  Therefore,  fyc. 

Or,  thus  :  At  1  per  cent.,  the  interest  of  $1  for  4  years  is 
4  cents,  and  of  $75  it  is  75  times  4  cents,  which  are  300 
cents,  equal  to  $3.  Since  $3  interest  is  1  per  cent,  of  $75 
for  4  years,  $18  interest  is  as  many  per  cent,  as  $3  is 
contained  times  in  $18,  which  is  6  times,  equal  to  6  per 
cent. 

2.  At  what  per  cent,  will  $200  gain  $49  interest 
in  3J  years  ? 

3.  At  what  per  cent,  will  $60  gain  $25  interest  in 
4^  years  ? 

4.  At   what   per   cent,  will  $90   gain   $27   in   6 
years  ? 


140  INTELLECTUAL   ARITHMETIC.  [94. 

5.  At  what   per   cent,   will   $12   gain  $5   in  Ifr 
years  ? 

6.  At  what  per  cent,  will  $400  gain  $55  interest 
in  2£  years  ? 

7.  At  what  per  cent,  will  $150  gain  $44  interest 
in  8|  years  ? 

8.  At  wiiat  per  cent,  will  $125  gain  $37.50  interest 
in  5  years  ? 

9.  At  what  per  cent,  will  $800  gain  $75  interest 
in  1  year  and  3  months  ? 

10.  At  what  per  cent,  will  $180  gain  $45  interest 
in  8  years  and  9  months  ? 

11.  At  what  per  cent,  will  $1250  gain  $312.50 
interest  in  2  years  6  months  ? 

12.  At  what  per  cent,  will  $2500  gain  $200  in- 
terest in  1  year  and  4  months  ? 

13.  At  what  per  cent,  will  a  given  principal  double 
itself  in  5  years  ? 

ANALYSIS.  Since  a  given  principal  must  gain  100  per 
cent,  to  double  itself  in  1  year,  to  double  itself  in  5  years  will 
require  ^  of  100  per  cent.,  or  20  per  cent.  Therefore,  fyc. 

14.  At  what  per  cent,  will  a  given  principal  double 
itself  in  10  years  ? 

15.  At  what  per  cent,  will  a  given  principal  double 
itself  in  12  years  6  months  ? 

16.  At  what  per  cent,  will  $200  double  itself  in  4 
years  ? 

17.  At  what  per  cent,  will  $100  double  itself  in  8 
years  ? 

18.  At  what  per  cent,  will  $150  double  itself  in 

15  years  ? 

19.  At  what  per  cent,  will  $500  double  itself  in 

16  years  8  months  ? 

20.  At  what  per  cent,  will  $175  double  itself  in 
2  years  6  months  ? 


95.]  INTELLECTUAL   ARITHMETIC.  141 

95.  The  present  worth  of  a  note  payable  at  a  future 
time  is  such  a  sum  as,  put  at  interest  at  the  given  rate  per 
cent,  until  it  becomes  due,  will  amount  to  the  face  of  the 
note. 

Discount  is  an  allowance  made  for  the  payment  of  money 
before  it  becomes  due,  and  is  obtained  by  subtracting  the 
present  worth  from  the  given  sum  or  face  of  the  note. 

1.  What  is  the  present  worth  of  $180  payable  in 
3  years  4  months  at  6  per  cent.  ? 

ANALYSIS.  Since  the  interest  for  3  years  4  months  at 
6  per  cent,  is  ±  of  the  principal,  (885)  the  amount,  $180, 
is  equal  to  the  principal,  -|,  added  to  the  interest,  -J,  equal  to 
f  of  the  principal.  Since  $180  is  f  of  the  principal,  ^  oj 
$180,  or  $30,  is  i,  and  $30  is  -i  of  5  times  $30,  or  $150. 
Therefore,  fyc. 

NOTE.  The  discount  is  the  difference  between  $180  and  $150,  which 
is  $30. 

2.  What  is  the  present  worth  of  a  note  for  836.90, 
payable  in  2  years  6  months,  at  5  per  cent.  ? 

3.  What  is  the  present  value  of  a  note  for  $54, 
due  in  5  years,  and  bearing  interest  at  7  per  cent.  ? 

4.  What  is  the  present  value  of  a  debt  of  $124.40, 
due  in  4  years  2  months,  at  8  per  cent,  interest  ? 

5.  What  is  the  discount  of  §2100,  due  in  1  year 
3  months,  at  4  per  cent.  ? 

6.  What  is  the  discount  on  a  note  of  $560,  paya- 
ble in  2  years,  at  6  per  cent,  interest  ? 

7.  What  is  the  difference  between  the  interest  and 
the  discount  of  $130,  due  10  months  hence,  at  10 
per  cent.  ? 

8.  A  man,  having  a  span  of  horses  for  sale,  offered 
them  for  $480  cash  in  hand,  or  a  note  of  $550  due 
in  1  year  8  months  without  interest.     The  buyer 
accepted  the  latter  offer  ?  did  the  seller  gain  or  lose 
by  his  offer,  and  how  much,  allowing  the  money  to 
be  worth  6  per  cent.  ? 


142  INTELLECTUAL   ARITHMETIC.  [96. 

96.  1.  B  sold  a  horse  for  |  of  1|  times  the 
cost ;  what  was  the  gain  per  cent.  ? 

2.  A  cow  purchased  for  $28  in  the  spring  was  sold 
for  $21  in  autumn  ;  what  was  the  loss  per  cent.  ? 

8.  An  old  lady  bought  80  apples  of  John  at  the 
lute  of  2  for  a  cent,  as  many  more  of  William  at  the 
rate  of  3  for  a  cent,  and  sold  the  whole  at  the  rate 
of  5  for  2  cents  ;  did  she  gain  or  lose,  and  at  what 
rate  per  cent.  ? 

4.  Did  she  gain  or  lose  on  the  purchase  made  of 
John  or  William,  and  at  what  rate  per  cent,  on  the 
amount  of  the  purchase  ? 

5.  A  hogshead  of  molasses  was  bought  for  $20 ; 
11^  per  cent,  of  it  leaked  out ;  how  must  the  re- 
mainder be  sold  per  gallon  to  gain  40  per  cent,  on 
the  cost  ? 

6.  A  manufacturer  sold  2  machines  for  $391  each  ; 
on  one  he  gained  15  per  cent.,  on  the  other  he  lost 
15  per  cent. ;  did  he  gain  or  lose  on  the  sale  of  both, 
and  how  much  ? 

7.  How  much  wheat  must  be  taken  to  mill,  that 
6  bushels  may  be  retained   after  riving  toll   of  6 
pounds  per  bushel,  or  10  per  cent,  for  grinding  ? 

8.  A  man  brought  home  1500  feet  of  lumber  after 
giving  37|-  per  cent,  of  the  whole  for  sawing ;  how 
much  lumber  did  he  have  sawed  ? 

9.  A  farmer  sold  2  horses  for  $150  apiece  ;  on  one 
he  gained  25  per  cent.,  on  the  other  he  lost  25  per 
cent. ;  did  he  gain  or  lose  on  both,  and  how  much  ? 

10.  For  hulling  barley,  36  per  cent,  is  taken  for 
pay ;  at  this  rate,  how  many  bushels  must  be  taken 
that  32  bushels  be  returned  after  hulling  ? 

11.  In  a  school   district  $57   was  to  be  collected 
for  teacher's  wages  ;  the  collector  was  to  have  5  per 
cent,  on  all  moneys  collected  ;  how  much  must  he 
collect  to  pay  his  fee  and  the  teacher  ? 


96.]  INTELLECTUAL    ARITHMETIC.  143 

12.  Hovi  much  plaster  must  A  have  ground,  to 
bring  home  14  tons,  after  the  miller  has  taken  12|- 
per  cent,  of  all  he  has  ground  ? 

13.  In  how  many  years,  at  5  per  cent.,  will  a 
given  principal  amount  to  the  same  as  it  would  at  7 
per  cent,  in  3  years  ? 

14.  At  what  rate  per  cent,  in  12  years  will  a  given 
principal  amount  to  the  same  as  at  7  per  cent,  for  8 
years  ? 

15.  A  farm  rents  for  $500  a  year,  which  is  6{  per 
cent,  on  the  purchase  money,  at  $40  per  acre ;  how 
many  acres  in  the  farm  ? 

16.  Mr.  Jones  paid  $44  interest  on  a  note  running 
4  years  4  months  and  24  days,  at  5  per  cent. ;  what 
was  the  face  of  the  note  ? 

17.  A's  note  of  $200  was  given  for  a  carriage  ;  5 
years  7  months  and  6  days  afterwards,   $256  was 
given  for  the  note  ;  what  rate  per  cent,  was  paid  ? 

18.  A  note  of  $300  on  interest  at  6  per  cent,  was 
given  for  a  span  of  horses  ;  when  the  note  was  taken 
up,  $330  was  paid  for  it ;  how  long  did  it  run  ? 

19.  B,  on  being  asked  how  much  he  owed  for  his 
farm,  replied,  "  I  pay  9  per  cent,  on  the  debt ;  if  I 
paid  but  7  per  cent.,  it  would  be  $60  in  my  favor 
yearly.''     What  did  he  owe  ? 

20.  If  Aaron  had  purchased  his  horses  for  5  per 
cent,  less  than  he  did,  they  would  have  cost  him  $190 ; 
how  much  did  he  pay  for  them  ? 

21.  If  I  had  purchased  my  farm  for  6  per  cent, 
less  than  I  paid  for  it,  it  would  have  made  a  differ- 
ence in  the  purchase  money  of  $120 ;  what  did  the 
farm  cost  me  ? 

22.  A  speculator  sold  wheat  for  90  cents  a  bushel, 
and  in  so  doing  lost  10  per  cent. ;  what  should  he 
have  sold  it  for,  to  have  gained  15  per  cent.  ? 

23.  A  nurseiynian  sold  apple   trees  at  $15   per 


144  INTELLECTUAL    ARITHMETIC.  [96. 

thousand,  and  cleared  |  of  his  receipts ;   what  per 
cent,  profit  did  he  make  ? 

24.  B  pays  $400  a  year  for  the  use  of  100  acres 
of  land,  giving  8  per  cent,  of  its  value ;  what  is  it 
worth  per  acre  ? 

25.  I  bought  a  stock  of  goods  for  $800,  and  paid 
#15  for  store  rent,  $85  for  clerk  hire,  and  sold  them 
at  the  end  of  6  months ;   what  per  cent,   must  be 
made  on  the  goods  to  cover  expenses  ? 

26.  In  how  many  years  will  a  man,  paying  inter- 
est at  7  per  cent,  on  a  debt  for  land,  pay  the  amount 
of  the  debt  in  interest  ? 

27.  A.  bought  a  form  for  $3000  ;  he  realized  $700 
from  the  sale  of  wheat,  $200  from  corn  and  barley, 
and  $100  from  fruit,  and  then  sold  the  farm  at  a  dis- 
count of  25  per  cent. ;  did  he  gain  or  lose,  and  how 
much  ? 

28.  B  bought  a  horse  for  $60,  then  sold  him  for 
$100,  and  repurchased  him  for  $80 ;  what  was  the 
gain  per  cent,  on  the  original  investment  ? 

29.  A  milkman  sold  milk  for  4  cents  a  quart,  by 
which  he  cleared  J  of  the  receipts ;  but  milk  becoming 
scarce,  he  sold  for  5  cents ;  what  per  cent,  did  he 
make  at  the  latter  price  ? 

30.  A  walked  5  per  cent,  of  a  journey  of  300  ^ 
miles ;  20  per  cent,  of  the  remainder  he  rode  in  the 
stage,  and  the  rest  of  the  way  in  the  cars ;  how  far 
did  he  ride  in  the  cars  ? 

31.  A  mechanic  sold  a  buggy  for  $54,  and  gained 
20  per  cent.  ;  he  then  sold  another  for  $54,  and  losit 
10  per  cent. ;  did  he  gain  or  lose,  and  how  much  ? 

32.  A  dealer  sold  a  melodeon  for  $190,  and  lost 
5  per  cent,  on  it ;  he  then  sold  another  for  the  same 
money,  but  made  enough  to  balance  the  loss  on  the 
first ;  what  per  cent,  did  he  make  on  the  second  ? 


97.]  INTELLECTUAL   ARITHMETIC.  145 

CHAPTER  IX. 

MISCELLANEOUS     EXAMPLES. 

97.  1.  A  gentleman,  owning  |  of  a  vessel,  sold 
I  of  his  share ;  what  part  of  the  vessel  does  he  still 
own? 

ANALYSIS.  Since  he  sold  £  of  his  share,  he  would  have  | 
lefty  and  £  of  ^  is  -J.  Therefore,  fyc, 

2.  A  man,  owning  ^  of  a  share  in  the  Central  Rail- 
road, sold  f  of  it ;  what  part  of  a  share  has  he  left  ? 

8.  A  man,  having  |  of  a  barrel  of  flour,  gave  £ 
of  it  to  a  poor  neighbor ;  what  part  of  a  barrel  has 
he  left  ? 

4.  Harry,  having  f  of  a  dollar,  gave  |  of  it  for  a 
knife ;  what  part  of  a  dollar  has  he  left  ? 

5.  A  man  sold  a  watch  for  $18,  which  was  |  of 
what  it  cost  him  ;  how  much  did  he  lose  ? 

6.  A  grocer  sold  a  quantity  of  cheese  for  $45, 
which  was  |  of  what  it  cost  him ;  how  much  did  he 
gain  ? 

7.  A  threshing  machine  was  sold  for  $120,  at  a 
sacrifice  of  f  of  the  cost ;  what  was  the  loss  on  it  ? 

8.  Henry  having  lost  -|  of  his  money  playing  cards, 
lent  ^  of  the  remainder,  when  he  found  he  had  $22 
left ;  how  much  had  he  at  first  ? 

9.  A  horse  was  sold  for  $80,  which  was  £  of  f  of 
twice  the  cost ;  what  was  lost  on  the  horse  ?~ 

10.  A  man  bought  a  wagon  for  $54,  which  was  $ 
of  twice  as  much  as  he  sold  it  for  ;  what  did  he  gain? 

11.  Homer  had  15  marbles,  which  was  f  of  3 
times  as  many  as  Henry  had  ;  how  many  had  Henry  ? 

12.  Thomas  gave  4  cents  for  a  top,  which  was  f 
times  J  of  what  money  he  had  ;  how  many  marbles, 
at  2  for  a  cent,  could  he  buy  with  what  he  had  left  ? 

10 


146  INTELLECTUAL   ARITHMETIC'.  [97. 

13.  A  farmer,  after  selling  I  of  his  flock  of  sheep, 
had  20  left ;  how  many  had  lie  at  first  ? 

14.  A  pole  was  standing  |  of  its  length  in  the  air, 
|  of  the  remainder  in  the  water,  and  3  feet  in  the 
mud  ;  how  many  feet  in  the  air  ? 

15.  If  from  my  age  you  take  \  and  f  of  my  age, 
the  remainder  will  be  4  years  ;  how  old  am  I  ? 

16.  If  to  f  of  the  cost  of  A's  coat  you  add  $12, 
the  sum  will  be  $20 ;  what  was  the  cost  of  the  coat  V 

17.  A  drover,  being  asked  how  many  sheep  he 
had,  replied,  "  If  to  J  my  number  you  add  80  sheep, 
the  sum  will  be  5  more  than  3  times  my  number ; " 
how  many  had  he  ? 

18.  John  and  James  play  at  marbles  ;  John  wins 
16,  which  is  f  of  twice  as  many  as  James  now  has  ; 
when  they  began,  |  of  John's  equaled  |  of  James's ; 
how  many  had  each  when  they  began  ? 

19.  J-  of  Herbert's  age,  increased  by  10  years, 
equals  1|  times  his  age  ;  how  old  is  he  ? 

20.  A  cow.  cost  $40  ;  f  of  this  sum  was  -^  of  2f 
times  \  of  the  cost  of  a  horse  ;  what  was  the  cost  of 
the  horse  ? 

21.  A.  was  25  years  of  age  when  he  was  married, 
and  his  age  was  |-  times  |  of  his  wife's  age  ;  how  old 
was  she  ? 

22.  A  post-office  was  robbed  by  a  clerk,  who  took 
-|  of  the  money  in  the  drawer  ;  when  he  was  arrested, 
he  had  made  away  with  f  of  it,  and  had  $10  left ; 
how  much  was  in  the  drawer  at  first  ? 

23.  A's  farm  cost  $1500  ;  f  of  this  is  f  of  4  times 
the  cost  of  the  barn  ;  what  did  the  barn  cost  ? 

24.  At  the  battle  of  Long  Island,  the  Americans 
lost  500  men  ;  |  of  this  number  was  |  of  J^-Q  of  their 
force  ;  how  many  men  had  they  in  the  field  ? 

25.  At  Ridge  field,  100  Americans  were  killed  ;  -f 
of  the  slain  was  7J-  times  y^  of  the  men  on  duty; 
how  many  on  duty  ? 


98.]  INTELLECTUAL   ARITHMETIC.  147 

26.  The  American  loss  at  the  battle  of  Trenton, 
in  killed,  frozen,  and  wounded,  was  60  men  ;  |  of 
this  number  was  2|  times  T^  of  the  number  en- 
gaged ;  how  many  men  in  the  engagement  ? 

27.  At  the  assault  on    Quebec,,  the  Americans  had 
100  killed;  f  of  this  number  was  6  more  than  If  times 
^  of  the  men  sent;  how  many  men  were  in  the  detach- 
ment ? 

28.  The  American  loss  in  the  battle  of  Port  Royal 
Island  was  30  men  ;   2^  times  this  number  was  3|- 
times  yV    of  the  number  in  the  field  ;  how  many  in 
the  field  ? 

29.  At  Germantown,  the  American  loss,  in  slain, 
wounded,  and  prisoners,  was  1200  ;  f  of  this  num- 
ber was  8|-  times  T|Q-  of  |  of  the  army,  lacking  1000 
men  ;  how  many  in  the  army  ? 


98.  1.  Divide  28  into  two  numbers  that'  shall 
be  to  each  other  as  5  to  2. 

ANALYSIS.  Since  the  numbers  are  to  each  other  as  5  to 
2,  the  given  sum  must  be  divided  into  7  equal  parts,  and  5  of 
those  parts  will  equal  one  of  the  numbers,  and  2  of  them  the 
other  ;  the  numbers  will  be  %  of  28  and  £  of  28,  equal  to  20 
and  8.  Therefore,  fyc. 

2.  Two  men  bought  40  bushels  of  potatoes  ;  one 
paid  $6,  and  the  other  $4 ;  how  many  bushels  should 
each  have  ? 

3.  Two  travelers,  49  miles  apart,  approach  each 
other ;  one  travels  4  miles  an  hour,  the  other  3  miles 
an  hour  ;  how  many  miles  will  each  travel  ? 

4.  A  and  B  hired  a  horse  and  buggy  for  $25  ;  A 
used  it  3  weeks,  B  2  weeks  ;  what  should  each  pay  ? 

5.  Two  men  hired  a  pasture  for  $24  ;  one  put  in 
5  cows?  the  other  put  in  3  cows ;  what  should  each 
pay? 


148  INTELLECTUAL   ARITHMETIC.  [98. 

6.  Two  men  hired  a  field  for  $12  ;  one  put  in  2 
horses  for  2  weeks,  the  other  two  horses  for  4  weeks ; 
what  should  each  pay  ? 

7.  John  had  9  cents,  and  Jay  had  7 ;  they  gave 
them  all  for  32  figs ;  how  many  hhould  each  of  them 
have  ? 

8.  A  and  B  enter  into  partnership  ;  A  invests  $10 
for  5  months,  B  invests  $5  for  8  months  ;  they  gain 
$45  ;  what  is  each  man's  bhare  of  the  gain  ? 

9.  A,  B,  and   C  bought  a  horse  ;  A  paid  $5  as 
often  as  B  $4  and  C  $3  ;  they  gained  $24  in  selling 
him  ;  what  is  each  man's  share  of  the  gain  ? 

10.  Three  men  agree  to  mow  a  field  for  $40  ;  A 
sends  2  men  three  days,  B  sends  3  men  three  days, 
C  sends  2  men  two  and  a  half  days  ;  what  should 
each  receive  ? 

11.  A,  B,  and  C  traded  in  company;  A  put  in 
$30,  B  $50,  and  C  such  a  sum  that  he  took  $10  of 
the  $42  gained  during  the  year  ;  what  was  the  gain 
of  A  and  B,  and  what  C's  stock  ? 

12.  An  ignorant  partner,  who  furnished  $500  of  a 
capital  of  $800,  on  which  $240  had  been  gained, 
took  $145  for  his  share  of  the  profits  ;  did  he  gain 
or  lose,  and  how  much  ? 

13.  Twro  men  paid  $11  for  the  use  of  a  pasture; 
the  first  put  in  5  calves,  the  second  4  colts  ;  what 
should  each  pay,  provided  2  colts  consume  as  much 
as  3  calves  ? 

14.  A,  B,  and  C  hire  a  field  for  $42  ;  A  puts  in  5 
cows,  B  3  cows,  and  C  pays  J  of  the  rent ;  how  much 
must  A  and  B  pay,  and  how  many  cows  does  C 
put  in  ? 

15.  Three  men  paid  $56  for  a  pasture  ;  the  first 
put  in  9  oxen,  the  second  8  cows,  and  the  third  10 
calves  ;  what  should  each  pay,  if  4  cows  eat  as  much 
as  3  oxen,  and  5  calves  as  much  as  4  cows  ? 


99.]  INTELLECTUAL   ARITHMETIC.  149 

16.  Mary  and  Melissa  wrote  60  lines  in  a  copy 
book  ;  Mary  wrote  £  as  many  lines  as  Melissa ;  how 
many  lines  did  each  write  ? 

17.  A   gardener   gave    24  pears   to  some  school 
children,  giving  each  girl  4  pears,  and  each  boy  3  ; 
the  boys  received  as  many  pears  as  the  girls ;  how 
many  children  were  there  ? 

18.  A  father  divided  $96  among  his  two  sons  and 
3  daughters,  giving  each  son  £  as  much  as   each 
daughter  ;  how  much  did  each  receive  ? 


99.  1.  Three  boys  have  76 marbles;  the  second 
has  2  more  than  the  first,  and  the  third  has  6  more 
than  the  second  ;  how  many  has  each  ? 

2.  James,  Henry,  and  Joseph,  together,  have  72 
apples ;  Henry  has  2  more  than  James,  and  Joseph 
2  more   than  Henry ;    if  each  had  110   more   than 
James,  how  many  would  all  have  ? 

3.  If   eacli   had  as  many  as  Joseph,   how  many 
would  all  have  ? 

4.  How  many  must  Joseph  give  James  that  each 
may  have  the  same  number  ?     How  many  has  each  ? 

*5.  A,  B,  and  C  built  a  warehouse  for  $600;  B 
paid  $100  more  than  A,  and  C  paid  as  much  as  A 
and  B  ;  how  much  did  each  pay  ? 

6.  William  bought  a  rifle,  a  watch,  and  a  drum, 
for  $42 ;  for  the  rifle  he  gave  twice  as  much  as  for 
the  drum,  and  for  the  watch  twice  as  much  as  for 
the  rifle  ;  what  did  he  give  for  each  ? 

7.  A  span  of   horses,  wagon,  and    harness    cost 
$225 ;  the  difference  between  the  cost  of  the  horses 
and  wagon  was  1^  times  the   cost  of  the  harness, 
and  the  cost  of  the  liorses  was  4  times  the  cost  of  the 
harness  ;  what  was  the  cost  of  each  ? 

8.  B  traveled  114  miles  in  3  days ;  the  first  day 


150  .       INTELLECTUAL   ARITHMETIC.  [99. 

he  traveled  |  as  far  as  on  the  last  2  days,  and  the  last 
clay  £  as  far  as  on  the  iirst  two  days  ;  how  far  did  he 
travel  each  day  '! 

9.  A  laborer  in  one  week  dug  5  rods  more  than 
|  the  length  of  a  ditch,  and  the  next  week  he  dug  the 
remaining  20  rods  ;  how  long  was  the  ditch  ? 

ANALYSIS.  Since  he  dug  5  rods  more  than  ±  of  the 
ditch  the  Jirst  week,  the  remainder,  20  rods,  increased  by  5 
rods,  must  equal  £  the  ditch ;  '20  rods  -j-  5  rods  =.  25  rods9 
which  is  £  of  twice  25,  or  50  rods.  Therefore,  fyc. 

10.  A  farmer,  owing  a  store  debt,  paid  at  0110 
time  $10  more  than    .l,  <>!'  it,  at  another   $20  more 
than  £  of  the  remainder,  and  gave  a  note  of  $20  for 
the  balance  of  the  debt ;  what  was  the  amount  of 
the  debt  ? 

11.  Arthur  gave  2  more  than  -*-  of  his  pennies  for 
a  top,  1  more  than  £  of  the  remainder  for  a  whip, 
and  had  4  left ;  how  many  pennies  had  he  at  first  ? 

12.  A  grocer,  selling  beer,  drew  -|-  a  gallon  more 
than  -|  the  contents  of  a  keg  one  day,  the  next  day 
he  drew  J  a  gallon  more  than  |-  of  the  remainder, 
and  the  third  day,  when  he  went  to  draw,  he  found  the 
keg  was  empty ;  how  many  gallons  in  the  keg  at  first  ? 

13.  A  and  B  have  $55  ;  £  of  A's  money  equals  f 
of  B's  ;  how  many  dollars  has  each  ? 

ANALYSIS.  Since  %  of  As  money  equals  §  of  B's,  2 
halves,  or  all  of  A's,  will  equal  2  times  -f,  or  §  of  It's  ;  then 
A  has  6,  and  S  5  equal  parts  of  the  money,  and  both  hai9 
11  parts  ;  T]T  of  $55  is  $5,  or\  part;  6  times  $5  are  $30, 
or  As  share  ;  and  5  times  $5  are  $25,  or  B's  share.  Ttiere- 
fore,  fyc. 

14.  If  34  apples  he  divided  between  John  and 
Mary,  so  that  f  of  John's  may  equal  |  of  Mary's, 
how  many  will  each  have  ? 


1OO.]  INTELLECTUAL   ARITHMETIC.  151 

15.  A  and  B  have  together  83  sheep ;   f  of  A's 
flock,  increased  by  8  sheep,  is  equal  to  B's  flock  ;  how 
many  sheep  has   each  ? 

16.  If  10  cents  be  taken  from  £  of  Mary's  money, 
the  remainder  will  be  equal  to  Susan's  ;  the  girls, 
together,  have  39  cents ;  how  many  cents  has  each  ? 

17.  Homer  has  3  marbles  more  than  Silas,  and  -| 
of  Homer's  marbles  equal  f  of  Silas's ;  how  many 
has  each  ? 


IOO.  1.  One  man  will  drink  a  gallon  of  beer  in  3 
days  ;  another  will  drink  a  gallon  in  4  days  ;  how  long 
will  a  gallon  last  both  of  them  ? 

2.  Julia  can  do   the  washing   in  7  hours  ;  with 
Jane's  assistance  she  can  do  it  in  4  hours ;  in  what 
time  can  Jane  do  it  ? 

3.  Two  boys  can  pitch  a  quantity  of  hay  in  5 
hours ;  the  first  can  do  it  in  9  hours  ;  in  what  time 
can  the  second  do  it  ? 

4.  A  cistern  can  be  emptied   by  2  pipes  in  3| 
hours,  but  1  pipe  will  empty  it  in  7^  hours  ;  in  how 
many  hours  will  the  other  empty  it  V 

5.  A  can  make  a  vest  in  |  of  a  day,  B  in  |,  and  0 
in  §  of  a  day  ;  how  many  more  vests  can  A  and  B 
make  in  a  day  than  C  can  ? 

6.  Susan  can  knit  a  pair  of  mittens  in  f  of  a 
day,  and  Sarah  can  knit  a  pair  in  |  of  a  day  ;  how 
many  pairs  can  both  knit  in  a  day  ? 

7.  What  part  of  a  day  must  Sarah  assist  Susan 
that  Susan  may  complete  2  pairs  ? 

8.  What  part  of  a  day  must  Susan  assist  Sarah 
that  Sarah  may  complete  3  pairs  ? 

9.  Jason  can  hoe  10  rows  of   corn  in  |  of   an 
hour,  and  Jesse  can  hoe  them  in  f  of  an  hour ;  in 
what  time  can  both  together  hoe  them  ? 


152  INTELLECTUAL   ARITHMETIC.  [1OO. 

10.  In  what  time  can  Jason  hoe  what  remains 
after  Jesse  has  hoed  |  an  hour  ? 

11.  In  what  time  can  Jesse   hoe  what  remains 
after  Jason  has  hoed  ^  of  an  hour  ? 

12.  How  many  rows  can  both  hoe  in  1  hour  ? 

13.  A  and  B  can  clear  a  field  in  15  days ;  with 
the  help  of  C  they  can  do  it  in  9  days ;  in  how  many 
days  can  C  do  it  ? 

14.  A  and  B  can  dig  a  well  in  6  days,  A  and  C  in 
8  days,  and  B  and  C  in  9  days ;  in  how  fhany  days 
can  each  dig  it,  working  alone  ? 

15.  In  how  many  days  can  they  do  it  working 
together  ? 

16.  Patrick,  Peter,  and  Philo  can  dig  40  rods  of 
ditch  in  10  days ;  Patrick  and  Peter  can  do  it  in  15 
days ;  Peter  and  Philo  can  do  it  in  13 J  days  ;  in  how 
many  days  can  Patrick  and  Philo  dig  28  rods  ? 

17.  How  long  will  it  take  each  man  to  dig  30  rods  ? 

18.  Henry  and  Harlan  can  cut  a  field  of  corn  in 
6f  days  ;  Harlan's  day's  work  exceeds  Henry's  by  ^ 
of  Henry's  ;  in  how  many  days  can  each  cut  the  field  ? 

19.  Three  men  can  do  a  piece  of  work  in  10  days ; 
the  first  does  f  as  much  as  the  second,  the  third  does 
I  as  much  as  the  first  and  second ;  in  how  many 
days  will  each  do  it  ? 

20.  In  how  many  days  will  the  first  and  second 
doit? 

21.  In  how  many  days  will  the  first  and  third  do  it  ? 

22.  In  how  many  days  will  the  second  and  third 
doit? 

23.  A,  B,  and  C  can  do  a  piece  of  work  in  8  days  ; 
B  and  C  can  do  it  in  12  days,  and  A  and  B  in  10 
days ;  in  how  many  days  can  each,  working  separately, 
doit? 

24.  A  cistern  can  be  discharged  by  3  pipes  in  4 
hours ;  the  first  and  second  pipes  will  discharge  it  in 


101.]  INTELLECTUAL   ARITHMETIC.  153 

8  hours  ;  the  first  and  third  in  6  hours  ;  in  what  time 
will  each  pipe  discharge  it  ? 

25.  Three  men  can  trench  a  field  in  10  days ;  A 
and  B  can  do  it  in  20  days  ;  B  and  C  can  do  it  in  15 
days ;  in  how  many  days  can  A  and  C  trench  the 
same  field  ? 

26.  A  barrel  of  flour  would  last  a  brother,  sister, 
and  servant  30  days ;  when  the  brother  was  absent 
it  would  last  60  days  ;  when  the  sister  was  absent  it 
would  last  45  days ;  how  long  would  it  last  the  sister 
after  all  had  used  from  it  20  days  ? 


1O1.  1.  Benjamin,  meeting  some  beggars,  gave 
each  of  them  5  cents ;  had  he  given  them  7  cents 
apiece,  it  would  have  taken  8  cents  more  ;  how  many 
beggars  were  there  ? 

ANALYSIS.  Since  2  cents  was  the  increase  paid  to  I 
beggar,  and  8  cents  the  increase  paid  to  all,  there  were  as 
many  beggars  as  2  is  contained  times  in  8,  which  is  4  times. 
TJierefore,  fyc. 

2.  Edward  gave  6  plums  to  each  of  his  playmates, 
and  had  9  remaining ;  had  he  given  each  of  them  8, 
he  would  have  had  but  1  left ;  how  many  playmates 
had  he  ? 

3.  Three  times  a  certain  number  is  15  less  than  6 
times  the  same  number  ?  what  is  the  number  ? 

4.  Susan,  purchasing   calico,  found   that  if   she 
took  that  at  8  cents  a  yard  she  would  have  11  cents 
left ;  but  if  she  took  that  at  12  cents  a  yard  she 
would  need  17  cents  to  pay  for  it ;  how  many  yards 
did  she  want  ? 

5.  4  times  a  number  is  15  less  than  6|-  times  the 
same  number  ;  what  is  the  number  ? 

6.  John,  being  asked  how  many  marbles  he  had, 
replied,  "  f  of  them  exceed  i  of  them  by  4."     How 
many  had  he  ? 


154  INTELLECTUAL   ARITHMETIC.  [1<H. 

7.  5J  times  a  number  is  21  greater  than  3|  times 
the  same  number  ;  what  is  the  number  ? 

8.  If  24  chestnuts  be  divided  among  some  boys, 
giving  4  apiece  to  J   of  them,  and  2  apiece  to  the 
others,  how  many  boys  are  tlu'iv  ': 

ANALYSIS.  Since  one  boy  received  4  chestnuts  as  often 
as  another  received  2  chestnut  s>  2  boys  received  j3  chestnuts', 
there  were  as  many  times  2  boys  as  6  is  contained  times 
in  24,  which  is  4  times,  and  4  times  2  boys  are  8  boys. 
Therefore,  fyc. 

9.  Mary  gave  her  chickens  26  grains  of  corn ;  f 
of  them  had  5  grains  each,  the  others  but  3  each ; 
how  many  chickens  had  she  ? 

NOTE.     The  above  gives  the  following  question  :  — 

10.  5  times  f  of  a  certain  number,  plus  3  times  J 
of  the  same  number,  is  26  ;  what  is  the  number  ? 

11.  A  class  received  29  merit  marks;  ^  of  them 
received  5  apiece,  |-  of  the  remainder  3  apiece,  f  of 
the  remainder  2  apiece,  and  the  rest  1  apiece ;  how 
many  scholars  in  the  class  ? 

12.  26  melons  were  stolen,  £  of  the  party  getting 
4  each,  the  rest  3  apiece,  except  2,  who  obtained  but 
2  apiece ;  how  many  were  there  in  the  party  ? 

ANALYSIS.  Had  the  last  2  obtained  3  each,  there  would 
have  been  28  melons ;  then  4  times  £  of  a  number,  plus  3 
times  £  of  the  same  number,  or  J,  icould  equal  28.  Since 
28  is  £  of  a  number,  $  of  28,  or  4,  is  £,  and  4  i s  £  of  2 
times  4,  or  8.  Therefore,  fyc. 

13.  4  times  |-  of  a  number,  plus  3J  times  the 
same  number,  is  equal  to  28  plus  5 ;  what  is  the 
number  ? 

14.  Henry  said  that  4  years  more  than  J  of  his 
age,  increased  by  5  times  ^  of  it,  and  that  sum  by  4 
times  ^  of  his  age  less  4,  would  make  the  sum  50 
years  ;  how  old  was  he  ? 


1O1.J  INTELLECTUAL   ARITHMETIC..  155 

15.  A  drover  paid  $5  a  head  for  J  of  his  flock,  $4 
a  head  for  as  many  more,  $3  a  head  for  |   of  the 
remainder,  and  $2  a  head  for  the  rest ;  the  flock  cost 
|115  ;  how  many  sheep  had  he  ? 

16.  A  grocer  received  $10  for  a  lot  of  baskets  ; 
for  J  of  them  he  had  6  dimes  each,  for  -|  of  the  re- 
mainder plus  3,  4  dimes  each,  for  J  of  the  rest  plus 
2,  3  dimes  each,  and  for  the  rest  2  dimes  each ;  how 
many  baskets  did  he  sell  ? 

17.  5  times  Henry's  age  is  3  more  than  4  times  | 
of  it  increased  by  6  times   •*-  of  it ;  how  old  is  he  ? 

ANALYSIS.  5  times  Henry's  age  equals  ±f,  4  times  §  of 
it,  plus  6  times  ^  of  it,  equals  -1/-,  and  if-  less  •*£  equals  £ 
of  it,  which,  according  to  the  conditions  of  the  question,  is 
3  ;  and  3  is  ^  of  3  times  3,  or  9.  Therefore,  fyc. 

18.  6  times  a  number  is  4  less  than  7  times  |  of 
it,  plus  5  times  ^  of  the  same  number ;  what  is  the 
number  ? 

19.  Bridget,  wishing  to  get  a  certain  number  of 
pounds  of  meat,  found,  if  she  took  beef  at  5  cents, 
she  would  have  4  cents  left ;  if  pork  at  7  cents,  she 
had  not  money  enough  to  pay  for  it ;  and  therefore 
she  took  |  of  the  quantity  in  beef,  the  rest  in  pork, 
and  paid  for  it ;  how  many  pounds  did  she  get  ? 

20.  Pour  times  a  number  is  6  greater  than  5  times 
|-  of  the  same  number  ;  what  is  the  number  ? 

21.  A  farmer,  wishing  to  buy  a  flock  of  sheep, 
found,  if  he  paid  $2  a  head,  he  would  have  $60  left ; 
if  he  paid  $5  a  head,  he  had  not  enough  to  pay  for* 
them  ;  if  he  took  |-  the  number  at  each  price,  he 
could  just  pay  for  them  ;   how  many  sheep  would 
his  money  buy  ? 

22.  Twice  f  of  a  number  equals  the  number  plus 
8  :  what  is  the  number  ? 


156  INTELLECTUAL   ARITHMETIC.  [1O3. 


1.   The  sum  of  two  numbers  is  27  ;  their 
difference  5  ;  what  are  tiie  numbers  ? 

ANALYSIS.  Since  27  is  the  sum  of  two  numbers  whose 
difference  is  5,  27  less  o,  or  22,  would  be  twice  the  less  num- 
ber ;  £  of  22  is  11,  £//<?  /ess  number,  which  increased  by  5 
equals  16,  or  Me  greater  number.  Therefore,  fyc. 

2.  James  and  John  together  have  19  peaches  ; 
John  has  3  more  than  James  ;  how  many  has  each  ? 

3.  Hobart  has  9  marbles  more  than  Herbert,  and 
together  they  have  31  ;  how  many  lias  each  ? 

4.  Two   men    are   37£   miles    apart,   and    travel 
toward  each  other  ;  when  they  meet,  one  has  trav- 
eled 5|  miles  more  than  the  other  ;   how  far  has 
each  traveled  ? 

5.  Horace,  finding  he  had  5  more  apples  than 
Homer,  gave  him  3,  when  they  together  had  21  ; 
how  many  had  each  then  ? 

6.  Mary  has  twice  as  many  berries  as  Martha,  and 
together  they  have  12  quarts  ;  how  many  quarts  has 
each  ? 

7.  A  farmer  had  47  sheep  in  two  fields  ;  in  one 
field  there  were  5  more  than  twice  as  many  as  in  the 
other  ;  how  many  were  there  in  each  field  ? 

8.  There  are  54  bushels  of  corn  in  two  bins  ;  in 
3ne  bin  there  are  6  bushels  less  than  half  as  many  as 
there  are  in  the  other  ;  how  many  bushels  in  each  ? 

9.  A  man  bought  a  watch  and  chain  for  $96  ;  the 
watch  cost  $4  less  than  3  times  the  cost  of  the  chain  ; 
what  was  the  cost  of  each  ? 

10.  Hiram  and  Harvey  built  wall  11  days  ;  Hiram 
received  2  dimes  a  day  more  than  Harvey,  and  they 
both  received  $25.30  ;  what  did  each  receive,  and 
how  much  per  day  ? 

11.  The  sum  of  A's  and  B's  ages  is  60  years  ;  6 
years  ago,  A's  age  was  J  of  B's  ;  what  are  their  ages 
now? 


IO2.]  INTELLECTUAL   ARITHMETIC.  157 

12.  A  horse  and  cow  cost  $124  ;  the  horse  cost 
$4  more  than  3  times  the  cost  of  the  cow ;  what  was 
the  cost  of  each  ? 

13.  A  farmer  paid  $24  for  a  colt  and  cow ;  ±  the 
cost  of  the  colt,  multiplied  by  ^  the  cost  of  the  cow, 
equaled  the  cost  of  the  cow ;  what  did  he  pay  for 
each  ? 

14.  A  lady  purchased  a  dish  and  cover  for  24 
dimes  ;   |  of  the  cost  of  the  dish,  increased  by  the 
difference  between  the  cost  of  the  dish  and  cover, 
equals  the  cost  of  the  cover ;  what  was  the  cost  of 
each  ? 

15.  A  grocer  purchased  25  pounds  of  butter  of 
two  women  ;  |  of  the  number  of  pounds  he  took  of 
one,  increased  by  the  difference  between  the  amounts 
purchased  of  both,  equals  the  number  of  pounds  he 
took  of  the  other  ;  how  many  pounds  did  each  sell  ? 

16.  The  sum  of  two  numbers  is  10  ;  their  differ- 
ence is  equal  to  ^  of  tfre  greater  number ;  what  are 
the  numbers  ? 

17.  A  wagon  cost  $38  ;  ^  of  the  cost  of  the  wood 
work  exceeds  the  cost  of  ironing  it  by  -l-  of  the  dif- 
ference between  the  expense  of  the  two ;  what  was 
the  cost  of  each  ? 

18.  Emily  purchased  some  lace  and  some  ribbon 
for  30  cents  ;  ^  the  cost  of  the  lace,  increased  by  ^ 
the  difference  between  the  cost  of  the  lace  and  rib- 
bon, equals  the  cost  of  the  ribbon ;  what  did  she  pay 
for  each  ? 

19.  Wilber  paid  20  shillings  for  a  pair  of  skates 
and  a  knife  ;  twice  the  difference  between  the  cost  of 
the  two,  plus  J  the  cost  of  the  knife,  equals  the  cost 
of  the  skates  ;  what  did  he  pay  for  each  ? 

20.  A  horse  and  harness  cost  $34  ;  |  of  the  cost 
of  the  horse  is  $1  more  than  the  cost  of  the  harness ; 
what  was  the  cost  of  each  ? 


158  INTELLECTUAL   ARITHMETIC.  [1O3. 

1O3.  1.  A  grocer  paid  812.60  for  30  bushels  of 
potatoes,  giving  50  cents  a  bushel  for  good  ones,  and 
20  cents  a  bushel  for  poor  ones ;  how  many  bushels 
were  good  ? 

ANALYSIS.  If  all  had  been  good,  he  would  have  paid 
$15,  or  $2.40  more  than  he  did;  each  bushel  of  poor  ones 
made  a  difference  of  30  cents;  hence  there  were  as  -many 
bushels  of  poor  ones  as  30  cents  (the  difference  on  1  bushel) 
is  contained  times  in  $2.40,  (the  difference  on  a//,)  which  is 
8  times,  equal  to  8  bushels  of  poor  ones  ;  the  difference  be- 
tween 30  bushels  and  8  bushels  is  22  bushels,  equal  to  the 
good  ones.  Therefore,  fyc. 

2.  A  fanner  bought  28  sheep  for  $76,  paying  $3 
for  old  sheep,  and  $2  for  yearlings ;  how  many  old 
sheep  ? 

3.  A  flour  merchant  paid    $82   for   20    barrels 
of  flour,  giving  $4.50  for  first   quality,  and   $3.50 
for  second   quality;   how   many   barrels  were   first 
quality  ? 

4.  Henry  sold  his  watch  for  $18,  and  by  so  doing 
lost  §  of  what  it  cost ;  what  did  it  cost  ? 

5.  A  man,  employing  an  equal  number  of  men 
and  boys,  paid  each  boy  5  dimes,  and  each  man  7 
dimes,  and  to  them  all  he  paid  $7.20 ;  how  many 
were  there  of  both  ? 

6.  An  old  lady  sold  an  equal  number  of  chickens 
and  turkeys  for  $4,  receiving  for  chickens  3  dimes 
each,  and  for  turkeys  5  dimes  each  ;  how  many  fowls 
did  she  sell  ? 

7.  A   speculator    bought    an    equal  quantity   of 
wheat  and  beans,  giving  $1.50  per  bushel  for  wheat, 
and  $1  for  beans ;  the  wheat  cost  $7  more  than  the 
beans  ;  how  many  bushels  of  beans  did  he  buy  ? 

8.  A  man  engaged  to  work  25  days,  on  condition 
that  he  should  receive  $2  for  every  day's  labor,  and 


1O3.]  INTELLECTUAL   ARITHMETIC.  159 

pay  $1  for  board  every  day  he  was  idle  ;  he  received 
at  settlement  $38 ;  how  many  days  was  he  idle  ? 

ANALYSIS.  As  many  days  as  $3,  (the  difference  made 
by  1  idle  day,}  is  contained  times  in  $12,  (the  difference 
made  by  all  the  idle  days,)  which  is  4  times,  llierefore  he 
was  idle  4  days. 

9.  A  man  was  engaged  for  20  days  to  copy,  re- 
ceiving $2.50  for  every  day's  labor,  and  forfeiting  $1 
for  every  day  lie  was  idle ;  he  received   $43 ;   how 
many  days  did  he  copy  ? 

10.  Job,  having  some  chestnuts,  gave  |  of  them 
to  John,  who,  after  eating  6,  gave  |  of  what  remained 
to  his  sister,  and  still  had  5  left ;  how  many  had  Job  ': 

ANALYSIS.  If  John  gave  £  to  his  sister,  the  5  left  was  £  ; 
5  is  £  of  4  times  5,  or  20,  and  20,  plus  the  6  he  ate,  make, 
26,  which  is  f  of  Job's,  fyc. 

11.  Mary  gave  ^  of  her  flowers  to  her  playmates, 
-|  of  the  remainder  to  her  teacher,  and  had  2  left ; 
how  many  had  she  at  first  ? 

12.  A  farmer  sold  |   of  1|  times  his  flock,  and 
had  12  sheep  remaining  ;  how  many  sheep  had  he 
at  first  ? 

13.  A  man  paid  $5  more  than  f  of  his  grocer's 
bill ;  soon  after  he  paid  -|  of  what  remained  unpaid, 
when   he  found   $3  was  still  due  ;    what  was  the 
amount  of  his  bill  ? 

14.  John  paid  $10  more  .than  J  of  his  year's 
wages  for  clothes,  $12  for  a  watch  ;  lie  then  lent  f 
of  what  he  had  left,  and  having  paid  $3  for  a  pair  of 
boots,  had  $5  left ;  what  were  his  wages  ? 

15.  A  laborer  engaged  to  work  20  days,  on  con- 
dition that  he  should  have  12  dimes  for  a  day's  labor, 
and  pay  2  dimes  for  every  idle  day  for  board  ;  he 
received  as  many  dollars  as  he  worked  days ;  how 
many  days  was  he  idle  ? 


160  INTELLECTUAL  ARITHMETIC.  [1O4. 

1O4.  1.  A  rope  28  feet  in  length  was  broken  so 
that  f  of  the  longer  piece  was  equal  to  the  shorter ; 
what  was  the  length  of  each  piece  ? 

ANALYSIS.  The  longer  piece  is  divided  into  5  equal 
parts,  2  of  which  equal  the  shorter ;  the  sum  of  the  2 
pieces  is  7  equal  parts,  one  of  which  equals  |  of  28  feet, 
or  4  feet ;  2  parts  equal  2  times  4  feet,  which  are  8  feet, 
the  shorter  piece  ;  5  parts  equal  o  times  4  feet,  which  are  20 
feet,  the  longer  piece.  Therefore,  fyc. 

2.  A  tree  56  feet  high  was  broken  in  a  storm  ;  |  of 
the  part  standing  was  equal  to  the  part  broken  off; 
what  was  the  length  of  each  part  ? 

3.  Henry  and  Horace  have  45  marbles  ;  Horace 
has  |  as  many  as  Henry  ;  how  many  has  each  ? 

4.  A  grocer,  having  opened  a  barrel  containing 
160  pounds  of  sugar,  took  out  |  as  much  as  he  left ; 
how  many  pounds  were  left  in  the  barrel  ? 

5.  A  traveler  paid  63   cents  for  his  supper  and 
fodging,  paying  f  as  much  for  his  supper  as  for  his 
lodging  ;  what  did  he  pay  for  his  supper  ? 

6.  A  horse  and  wagon  cost  $170 ;  the  horse  cost 
1-J-  times  as  much  as  the  wagon  ;  what  was  the  cost 
of  each  ? 

7.  Henry  traveled  140  miles  in  2  days  ;  the  first 
day  he  traveled  1^  times  as  far  as  he  did  the  second  ; 
how  far  did  he  travel  each  day  ? 

8.  From  Buffalo  to  Bergen  is  50  miles,  from  Bergen 
to  Utica  is  1|  times  as  far  as  from  Utica  to  Schenec- 
tady,  which  is  280  miles  from  Buffalo  ;  how  many 
miles  from  Buffalo  to  Utica  ? 

9.  David  caught  a  trout  17  inches  long ;  the  tail 
was  -|  as  long  as  the  body,  and  the  head  was  3  inches 
long ;  how  long  was  the  tail  ? 

10.  Divide  36  into  2  such  parts   that  1|   times 
one  shall  equal  the  other. 


104*]  INTELLECTUAL   ARITHMETIC.  161 

11.  Homer  and   Harlan   have   48   apples ;    £  of 
Homer's,  plus  6,  equal     the  number  Harlan  has; 
how  many  has  each  ? 

ANALYSIS.  Harlan  has  6  more  than  £  as  many  as  Ho- 
mer, which  makes  the  sum  48,  6  greater  than  if  he  had  but 
%  as  many ;  Homer's  are  divided  into  4  parts,  of  which  3 
parts  plus  6  apples  are  equal  to  Harlan' s ;  then  4  parts 
plus  3  parts,  plus  G  apples,  equal  48,  7  parts  equal  42, 
and  y  of  42,  or  6,  equals  1  part.  3  parts  plus  6  equal 
24,  the  number  Harlan  has,  and  4  parts  equal  24,  the  num- 
ber Homer  has.  Therefore,  fyc. 

12.  Rochester  is  52  miles  from  Geneva,  via  Vic- 
tor ;  i5y  of  the  distance  from  Geneva  to  Victor,  plus 
4  miles,  equals  the  distance  from  Victor  to  Roches- 
ter ;  how  far  is  Victor  from  each  place  ? 

13.  From  the  ground  to  the  top  of  a  church  steeple 
is  146  feet ;  |  of  the  height  of  the  steeple  above  the 
church,  plus  6  feet,  is  equal  to  the  height  of  the  church; 
•what  is  the  height  of  the  steeple  above  the  church  2 

14.  A  jar  and  cover  weigh  18  pounds ;  -|  of  the 
weight  of  the  cover,  increased  by  12  pounds,  equals 
the  weight  of  the  jar  ;  what  is  the  weight  of  each  ? 

15.  A  coat  and  vest  cost  $19  ;  ^  of  the  cost  of  the 
coat,  plus  $3,  equals  the  cost  of  the  vest ;  what  is  the 
cost  of  each  ? 

16.  Wilson  has  15  oranges  and  lemons ;  J  of  the 
oranges  equals  ^  of  the  lemons ;  how  many  "of  eacli 
has  he  ? 

ANALYSIS.  Since  ^  of  the  oranges  equals  -J  of  the  lemons, 
f ,  or  all  the  oranges,  equal  §  of  the  lemons ;  we  then  have 
the  oranges  and  lemons  divided  into  5  equal  parts,  2  parts 
of  which  equal  the  oranges,  and  3  the  lemons,  $c. 

17.  A   father   gave   his   2   sons   50   cents;   l   of 
George's  money  was  equal  to  f  of  Abel's  ;  how  many 
cents  had  each  ? 

18.  Andrew  has  84  marbles ;  -|  of  the  gray  ones 

11 


162  INTELLECTUAL   ARITHMETIC.  [1O4. 

equal  £  of  the  black  ones  ;  how  many  of  each  kind 
were  there  ? 

19.  The  sum  of  two  numbers  is  62 ;   |   of  one 
equal  |  of  the  other ;   what  are  the  numbers  ? 

20.  A  purse  and  contents  are  valued  at  46  shil- 
lings ;  |  of  the  value  of  the  purse  is  equal  to  |  of 
the  value  of  what  is  in  it ;  what  is  the  purse  worth  ? 

21.  A  person,  being  asked  the  time  of  day,  replied, 
"  The  time  past  noon  is  equal  to  |  of  the  time  to 
midnight."     What  was  the  hour  ? 

ANALYSIS.  The  time  to  midniyht  is  divided  into  5  equal 
parts,  one  of  which  equals  the  time  past  noon  ;  then  5  parts 
pins  1  part  equals  6  parts  \and-  12  Itours,  the  time  from 
noon  to  midnight,  must  be  ^  of  the  time  it  lacked  of  being 
midnight ;  since  12  is  f ,  -£,  which  is  £  o/f,  will  be  £  of  12 
hours,  which  is  2  hours.  Therefore  the  hour  was  2  o'clock, 
P.M. 

22.  What  was  the  time,  provided  f-  of  the  time 
past  midnight  equaled  the  time  to  10  o'clock,  A.  M.? 

23.  |  of  the  time  from  this  instant  to  5  o'clock, 
P.  M.,  equals  f  of  the  time  past  midnight;  what  is 
the  time  of  day  ? 

24.  Peter  said  to  John,  "  If  times  my  age  is  1| 
times  your  age,  and  the  sum  of  our  ages  is  36  years." 
What  was  the  age  of  each  ? 

25.  A  bin  whose   capacity  was  44   bushels  was 
partly  filled  with  grain  ;  2|  times  what  was  in  it  was 
2|  times  what  it  would  take  to  fill  it ;  how  many 
more  bushels  would  fill  it  ? 

26.  A  person,  inquiring  the  distance  to  Cincinnati, 
was  told  that  3|-  times  what  it  lacked  of  being  83 
miles  was  1-|  times  what  it  exceeded  39  miles ;  how 
far  was  he  from  Cincinnati  ? 

27.  The  number  of  miles  that  the  distance  from 
Charleston  to  Columbia  exceeds  100  miles  equals  1J 
times  the  distance  it  lacks  of  being  150  miles  :  how 
far  is  it  from  Charleston  to  Columbia  ? 


1OO.]  INTELLECTUAL   ARITHMETIC.  163 

1O»>«  1.  Two  pieces  of  cloth  contain  38  yards; 
|  of  the  first  piece  equals  -f  of  the  second,  plus  4 
yards  ;  how  many  yards  in  each  piece  ? 

ANALYSIS.  If  §  equal  f  -f-  4,  ^  wz7/  e^waZ  £  o/1  §  -j-  4, 
wAicA  is  -i  +  2,  Jfo's  zs  £  of  3  times  -£  +  2,  or  f  -|-  6 ; 
tf^ew  we  Aaz?e  1  piece  equal  to  f  ^e  other  plus  6  yards,  or  1 
pzece  divided  into  5  parts,  and  3  of  these  parts  plus  6  yards 
equal  the  other  piece  ;  hence  5  parts  plus  3  j0ar&  plus  6  yards 
equal  38  yards,  or  8  /?ar£s  ano?  6  yards,  equal  38  yards  ;  38 
yards  minus  6  yards  equal  32  yards,  or  8  parts,  fyc. 

2.  A  lad  inquiring  his  mother's  age,  his  father 
replied,  u  f  of  my  age  is  9  years  more  than  |-  of 
your  mother's,  and  the  sum.  of  our  ages  is  72  years." 
How  old  was  his  mother  ? 

8.  Two  men  built  38  rods  of  wall ;  |  of  what  one 
built,  plus  4  rods,  is  equal  to  |  of  what  the  other 
built ;  how  many  rods  did  each  build  ? 

4.  Hiram  and  Richard  sheared  67  sheep ;  |  of  the 
number  Hiram  sheared  was  4  more  than  -|  of  the 
number  Richard  sheared  ;  how  many  did  each  shear  ? 

5.  What  is  the  time,  providing  |  of  the  time  past 
midnight,  plus  1-^  hours,  equals  |  of  the   time  to 
midnight  ? 

6.  A,  being  asked  his  age,  replied,  "  1|-  times  what 
I  lack  of  being  a  hundred  years  old  is  9  years  more 
than  1|-  times  what  my  ago  exceeds  64."     What  was 
his  age  ? 

7.  A  rope  was  cut  into  3  pieces;  the  first  piece 
was  5  feet  long,  the  second  was  as  long  as  the  first 
plus  I  of  the  third,  and  the  third  was  as  long  as  the 
other  two ;  what  was  the  length  of  the  rope*  ? 

ANALYSIS.  Since  the  third  piece  is  as  long  as  the  other 
two,  it  must  be  ^  of  the  rope ;  the  second  piece,  being  £  as 
long,  is  ^ ;  and  the  5  feet  which  the  second  exceeds  J,  with 
the  5  feet  of  the  first  piece,  make  10  feet,  which  must  be  the 
other  fourth  ;  4  times  10  is  40.  Therefore,  fyc. 


164  INTELLECTUAL   ARITHMETIC. 

8.  The  head  of  a  fish  is  7  inches  long,  the  tail  is 
as  long  as  the  head  and  i  of  the  body,  and  the  body 
is  as  long  as  the  head  and  tail ;  what  is  the  length  of 
the  fish  ? 

9.  A  piece  of  steel  was  broken  into  3  pieces;  the 
first  piece  was  j-  of  the  whole,  the  second  weighed  3 
pounds,  and  the  third  weighed  as  much  as  the  other 
two  ;  what  was  the  weight  of  the  whole  ? 

10.  Three  men  dig  potatoes ;  the  first  digs  ^  of 
the  whole,  lacking  2  bushels,  the  second  digs  5  bush- 
els, and  the  third  digs  as  many  as  the  other  two ; 
how  many  bushels  did  all  dig  ? 

11.  From  Batavia  to  Avon  is  24  miles ;  this  dis- 
tance, plus  the  distance  from  Bath  to  Corning,  and 
12  miles  more,  equals  the  distance  from  Avon  to 
Bath  ;  from  Bath  to  Corning  is  \-  of  the  whole  dis- 
tance ;  how  far  from  Batavia  to  Corning  ? 

12.  A  farmer  took  money  for  stock,  as  follows : 
$18  for  swine,  $6  more  than  £  of  the  whole  for  sheep, 
and  for  cattle  $7  less  than  f  as  much  as  for  sheep 
and  swine  ;  how  many  dollars  did  he  receive  ? 

13.  A  third  and  *  a  third  of  12  is  f  of  twice  what 
number  ? 

14.  Stephen  spent   ^   of  his   money,  and  afterward 
earned  £  as  much  as  he  had  spent,  when  he  had  $16.50 
less  than  at  first ;  how  much  had  he  at  first  ? 

15.  If  |  of  a  ton  of  hay  cost  f  of  an  eagle,  how 
many  dollars  will  £  of  a  ton  cost  ? 

16.  A  is  6  years  more  than  -|-  as  old  as  B,  C  is  | 
as  old  as  A,  and  B's  age  is  equal  to  the  sum  of  A's 
and  CV;  what  is  the  age  of  each  ? 

17.  A  owns  12  more  than  f  as  many  acres  as 
B,  C  owns  £  as  many  as  A,  and  B  owns  24  acres 

than  A  and  C ;  how  many  acres  has  each. 


1OO.]  INTELLECTUAL   ARITHMETIC.  1G5 

1O6.  1.  Malcom  is  8  years  old,  and  Martin  25  ; 
in  how  many  years  will  Malcom  be  -|  as  old  as 
Martin  ? 

ANALYSIS.  8  years  since,  Martin  was  17  years  of  age; 
in  17  years  from  that  time,  or,  since  Malcom  is  8  years  old, 
in  17  less  8,  or  9  years  from  this  time,  Malcom  will  be  17 
years  old,  and  Martin  will  be  twice  17,  or  34  years  old. 
Therefore,  fyc. 

2.  A  father  is  22  years  older  than  his  son,  and  the 
son's  age  is  f  of  the  father's ;  how  many  years  since 
the  son's  age  was  J  the  father's  ? 

3.  Helen  is  9  years  old,  her  sister  is  22  ;  in  now 
many  years  will  Helen  be  -£  as  old  as  her  sister  ? 

4.  Henry  played  at  marbles  with  Charles,  who 
had  45  ;  Henry  won  as  many  as  he  had  to  commence 
with  ;  when  they  quit,  each  had  the  same  number  ; 
how  many  had  both  ? 

ANALYSIS.  Since  Henry  won  as  many  as  he  had,  he  left 
off  playing  with  twice  as  many  as  he  began  with  ;  and  Charles, 
now  having  the  same  number,  must  have  had  3  times  as 
many  as  Henry  when  they  commenced  playiny.  45  is  3 
times  -J  of  45,  or  15,  and  45  -\-  15  is  60.  Therefore,  fyc. 

5.  A  farmer,  having  60  sheep  in  one  field,  took  as 
many  from  them  as  he  had  in  another  field,  and  put 
them  with  the  others,  when   the  flocks  were  equal ; 
how  many  sheep  had  he  ? 

6.  From  a  bin  containing  52  bushels,  2  more  than 
as  many  bushels  as  were  in  another  bin  were  taken 
and  put  in  the  other  bin,  when  both  contained  the 
same  quantity  ;  how  many  bushels  in  both  bins  ? 

7.  Uncle  Simon's  age,  increased  by  the  difference 
between  -|  and  %  of  his  age,  is  6  more  than    ^  times 
his  age  ;  how  old  is  he  ? 

8.  Henry  earned  20  dollars  in  the  spring ;  in  the 
fall  he  earned  as  much  as  in  the  spring  and  £  as 


10(3  INTELLECTUAL   ARITHMETIC.  [1O6. 

much  as  in  the  summer,  and  in  the  summer  as  much 
as  in  the  spring  and  fall ;  how  much  did  he  earn  in 
all? 

9.  A  has  10  sheep,  C  has  as  many  as  A  and  |  as 
many  as  B,  and  B  has  as  many  as  A  and  C  ;  how 
many  sheep  have  they  all  ? 

ANALYSIS.  Since  B  has  as  many  as  A  and  C  he  muit 
have  ±  of  the  ivltole  ;  then  10  sheep,  plus  10  -f~  %  °f  i» 
phis  ±,  equals  %  -\-  20,  or  the  whole  number  of  sheep  ;  hence 
20  equals  £  the  number,  and  20  is  \  of  6  times  20,  or  120 
sheep.  Therefore,  fyc. 

10.  A,  owning  74  acres  of  land,  sold  B  |  as  much 
as  B  owned ;  then  B's  farm  was  f  as  large  as  A's ; 
how  many  acres  in  each  farm  ? 

11.  Mary  has  10  more  chickens  than  turkeys,  yet 
|  of  the  turkeys   equal   \  the  chickens  ;  how  many 
chickens  has  she  ? 

12.  Hainan's  coat  cost  $15  less   than   his  whole 
suit ;  ^  of  the  price  of  the  suit  equaled  |  of  the  price 
of  the  coat ;  what  did  the  suit  cost  ? 

13.  Daniel   caught   14    pigeons   more    than    his 
brother,  and  2f  times  his  brother's  equaled  |  of  his  ; 
how  many  did  each  catch  ? 

14.  One  number  is  31  times  another ;    if  15  be 
added  to  each,  one  is  just  ^  of  the  other;  what  are 
the  numbers  ? 

15.  The  difference  between  the  cost  of  a  horse 
and  a  buggy  is  $40  ;  |  of  the  cost  of  the  buggy  equal 
-^5   of  the  cost  of  the  horse ;  what  is  the  value  of 
each  ? 

16.  Alice  is  l  as  old  as  her  mother  ;  5  years  since 
she  was  but  ^  as  old  ;  in  how  many  years  will  she  be 
J  as  old  ? 

IT.  Hobart,  having  20  marbles  more  than  Dwight, 
plays  with  him  ;  Dwight  wrins  |-  as  many  as  he  had 


1O7.]  INTELLECTUAL   ARITHMETIC.  16T 

at  first,  when  Hobart  lias  |-  as  many  left  as  he  com- 
menced with  ;  how  many  had  each  at  first  ? 

18.  The  difference  between  two  numbers  is  16 ; 
if  4  be  taken  from  the  larger  and  added  to  the  less, 
2 1  times  the  larger  will  equal  3J  times  the  smaller; 
what  are  the  numbers  ? 

19.  Jason  bought  a  watch,  and  had  820  remain- 
ing ;  he  then  gave  2   times  the  cost  of  the  watch  for 
a  rifle,  and  had  -^  of  his  money  left ;  what  did  the 
rifle  cost  ? 

20.  Find  the  ages  of  A,  B,  and  C,  by  knowing 
that  C's  age  at  A's  birth  was  5J  times  B's,  and  now 
is  equal  to  the  sum  of  A's  and  B's ;  also  that  if  A 
were  now  3  years  younger,  or  B  4  years  older,  A's 
age  would  be  equal  to  |  of  B's. 


1O7.  1.  Two  boys  are  running  in  the  same 
direction ;  one  is  27  rods  in  advance  of  the  other  in 
pursuit,  who  gains  upon  the  foremost  3  rods  in  a 
minute  ;  in  how  many  minutes  will  he  be  overtaken  ? 

ANALYSIS.  In  as  many  minutes  as  3,  the  number  of  rods 
gained  in  one  minute,  is  contained  times  in  27,  the  number 
of  rods  to  be  gained. 

2.  A,  after  traveling  2  hours,  at  the  rate  of  5 
miles  an  hour,  was  followed  by  B,  at  the  rate  of  7 
miles  an  hour ;  in  how  many  hours  would  B  over- 
take A  ? 

3.  A  dog  in  pursuit  of  a  hare  which  has  28  rods 
the  start,  runs  9  rods  while  the  hare  runs  7  ;  how  far 
will  the  dog  run  to  catch  the  hare  ? 

4.  Henry  saves  $5  while  John    saves   $ 7 ;    how 
much  will  each  have  when  the   difference  between 
what  each  has  saved  is  $30  ? 

5.  A  and  B  started  from  the   same  point  to  run  a 
race ;  A  ran  84  rods  and  gave  out,  when  ^  of  the 


168  INTELLECTUAL   ARITHMETIC.  [1O7, 

distance  B  had  run  equaled   the  distance  he  was 
ahead  of  A ;  how  far  did  B  run  ? 

G.  Three  men  bought  a  horse  ;  A  paid  $25,  which 
was  ^  of  what  B  and  C  paid ;  B  paid  |  as  much  a& 
A  and  C  ;  what  did  B  and  C  pay  ? 

7.  The  hour  and  minute  hands  of  a  watch  aro 
together  at  12  o'clock ;  when  will  they  next  be  to- 
gether ? 

ANALYSIS.  Since  the  minute  hand  passes  the  hour  hand 
11  times  in  12  hours,  if  both  are  at  12,  the  minute  hand  will 
pass  the  hour  hand  the  jirst  time  in  -Jf  of  1 2  hours,  or  in 
l^Y  hours,  equal  to  5^  minutes  past  1  o'clock.  There- 
fore, $c. 

8.  A  gentleman,  being  asked  the  time,  replied, 
"  It  is  between  3  and  4  o'clock,  and  the  hands  are 
directly  opposite."     What  was  the  time  ? 

9.  A  fox  is  40  leaps  ahead  of  a  hound,  and  takes 
7  leaps  to  the  hound's  4 ;  but  3  of  the  hound's  leaps 
equal  6  of  the  fox's ;  how  many  leaps  will  the  fox 
take  before  being  caught  ? 

10.  A  wolf  ran  80  rods  to  catch  a  sheep  ;  f  of  the 
distance  the  sheep  ran  was  equal  to  the  distance  be- 
tween them  when  the  chase  commenced  ;   what  was 
the  distance  ? 

11.  The  sum  of  f  of  A's  and  f  of  B's  money,  being 
on  interest   2  years  7  months  and  6  days,  at  5  per 
cent.,  amounted  to  $2260 ;    f  of  B's  money  was  \\ 
times  f  of  A's  ;  how  much  had  each  ? 

12.  B's  fortune  is  1J  times  A's  ;  the  interest  of  \ 
of  A's  fortune  and  \  of  B's  for  5  years,  at  6  per  cent., 
is  $600  ;  what  is  the  fortune  of  each  ? 

13.  A  drover  paid  $76  for  calves  and  sheep,  pay- 
ing $3  apiece  for  calves  and  $2  for  sheep  ;   he  sold  \ 
of  his  calves  and  f  of  his  sheep  for  $23,  and  in  so 
doing  lost  8  per  cent,  on  their  cost ;   how  many  of 
each  did  he  purchase  ? 


APPENDIX. 


THE  author  desires  to  call  the  attention  of  teachers  to  the  numbered 
Tariety  of  changes  that  may  be  wrought  upon  the  examples  of  the  Sec. 
tions  from  which  the  following  have  been  selected,  as  well  as  upon  many 
otheis  of  the  same  class,  and  which  may  appropriately  be  termed  "  Ring- 
ing the  Changes."  It  is  not  recommended  that  these  changes  be  ap- 
plied to  ail  the  examples,  but  used  as  an  occasional  exercise,  and  limited 
according  to  the  time  and  convenience  of  the  teacher. 

It  is  recommended  to  teachers  to  exercise  their  classes  in  these 
*  changes,"  not  so  much  for  the  novelty  of  them,  as  for  the  enlivening 
effect  produced  upon  the  class,  and  especially  for  the  peculiar  facilities 
they  afford  for  thorough  mental  discipline  ;  and  while,  at  first,  to  some 
they  may  appear  severe  and  too  mathematical,  they  will  very  soon  become 
easy  and  comprehensible. 

To  aid  beginners,  the  blackboard  may  be  used  to  advantage  ;  and  to 
illustrate,  take  the  example  which  has  been  written  out  in  full  in  Section 
715  page  171-3:  — 

4-  of  35  is  I  of  how  many  thirds  of  18  ? 
which  may  be  written  on  the  board  thus  :  — 

f  x  35  =  f  X  7  X  18? 

Call  upon  seme  pupil  to  read  the  question  according  to  thejfost  form, 
and  to  solve  the  question  according  to  the  form  of  analysis  given  ;  and 
the  answer,  if  correct,  placed  over  the  3,  will  fulfill  the  conditions  of  th« 
question;  substitute  this  number,  and  erase  another,  thus  :  — 


which  is  read 

4.  of  35  is  f  of  f  of  what  number  ? 

Solve  this  as  before,  and  so  continue  until   all  the  numbers  have  been 
erased,  and  replaced  by  solution. 

AVhen  the  class  have  become  familiar  with  the  exercise,  the  use  of  the 
blackboard  should  be  dispensed  with,  and  the  pupil  be  required  to  "  ring 
the  changes  "  by  simply  hearing  the  first  form  of  the  question  read. 

Each  question,  and  its  form  of  solution,  should  be  given  by  the  pupil, 
but  he  may  be  allowed  to  give  results  in  the  solution  that  have  been 
previously  determined  by  analysis,  in  order  to  shorten  the  work  and  avoid 
monotonous  repetition. 

Members  of  the  class  should  be  called  upon  promiscuously,  and  en- 
couraged to  ask  questions,  and  to  detect  errors  either  in  the  statement  or 
solution  of  questions.  The  teacher  should  read  an  example  once,  slowly 
and  distinctly,  then  call  upon  some  one  of  the  class  who  shall  commence 
operations,  and  continue  to  give  questions,  forms,  solutions,  and  conclu- 
sions, until  signaled  to  sit,  or  another  pupil  detecting  an  error,  raises 
the  hand,  when  some  other  one  should  be  called  upon,  who  should  re- 
sume where  the  last  one  left  off;  and  so  on. 

A  teacher  who  has  not  practiced  a  class  upon  these  changes,  cannot 
conceive  of  the  interest,  close  attention,  and  perfect  enthusiasm  that 
may  be  created,  as  well  as  the  thorough  mental  discipline  attained,  by  this 
exercise  ;  and  it  is  firmly  believed  that,  upon  trial,  it  will  commend  itself 
to  the  judgment  and  approval  of  every  live  teacher. 

12  (169) 


170  APPENDIX. 

67.     1.    24  is  £  of  how  many  times  10  ? 

24  is  |  of  as  many  times  10  as  10  is  contained  times  in 
5  times  :}  of  24  ;  J  of  24  is  6,  and  5  times  6  is  30;  10  is 
contained  in  30,  3  times.  Therefore  24  is  i  of  3  times  10. 

2.  24  is  f  of  3  times  what  number  ? 

24  is  1  of  -3  times  .'.  of  5  times  \  of  24 ;  \  of  24  is  6, 
and  5  times  G  is  30  ;  •]•  of  30  is  10.  Therefore  24  is  / 
of  3  times  10. 

3.  24  is  how  many  fifths  of  3  times  10  ? 

24  is  as  many  fifths  of  3  times  10  as  £  of  3  times  10  is 
contained  limes  in  L>4.  3  times  10  is  30,  and  -J-  of  30  is 
0,  and  (')  is  contained  in  24,  4  times.  Therefore  24  is  A 
of  3  times  10. 

4.  24  is  4  times  what  part  of  3  times  10  ? 

24  is  4  times  such  a  part  of  3  times  10  as  3  times  10 
is  contained  times  in  -J  of  24.  3  times  10  is  30.  and  \ 
of  24  is  6  ;  30  is  contained  in  C,  /„  or  1  times.  There- 
fore 24  is  4  times  i,  or  |,  of  3  times  10. 

5.  What  number  is  f  of  3  times  10  ? 

4  times  i  of  3  times  10.  3  times  10  is  30,  l  of  30  is  C, 
and  4  times  6  is  24.  Therefore  24  is  4  of  3  times  10. 


7O.     1.  4  of  56  is  -J-  of  3  times  what  number  ? 

4  of  56  is  |  of  3  times  -J-  of  9  times  £  of  4  times  -\ 
of  56  ;  i  of  56  is  8,  and  4  times  8  is  32  ;  £  of  32  is  4, 
and  9  times  4  is  36  ;  -J  of  36  is  12.  Therefore,  -$  of  56 
is  |  of  3  times  12. 

2.  4  of  56  is  £  of  how  many  times  12  ? 

|  of  56  is  §  of  as  many  times  12  as  12  is  contained 
times  in  9  times  J-  of  4  times  £  of  56 ;  4  °f  56  is  8?  an^ 
4  times  8  is  32  ;  i  of  32  is  4,  and  9  times  4  is  36  ;  12  is 
contained  in  36,  3  times.  Therefore  ^  of  56  is  |  of  3 
times  12. 

3.  4  of  56  is  how  many  ninths  of  3  times  12  ? 

4  of  56  is  as  many  ninths  of  3  times  12  as  ^  of  3  thru."? 


APPENDIX.  171 

12  is  contained  times  in  4  times  *  of  50.  ^  of  56  is  8, 
and  4  of  56  is  4  times  8  ;  4  times  8  is  32  ;  3  times  12 
is  36,  ^  of  36  is  4,  and  4  i-?  contained  in  32,  8  times. 
Therefore  |  of  56  is  f  of  3  times  12. 

4.  4  °f  5(>  is  8  times  what  part  of  3  times  12  ? 
Such  a  part  of  3  times  12  as  3  times  12  is  contained 

times  in  |  of  4  times  %  of  56.  ^  °f  56  is  8,  and  4  times 
8  is  32  ;  £  of  32  is  4  ;  3  times  12  is  36,  and  36  is  con- 
tained in  4,  ^j  or  ^  times.  Therefore  ^  of  56  is  8  times 
^,  or  |,  of  3  times  12. 

5.  f  of  3  times  12  is  -f  of  what  number  ? 

|  of  3  times  12  is  ^  of  7  times  j  of  8  times  -g  o.  3 
times  12  ;  £  of  36  is  4,  and  8  times  4  is  32  ;  |  of  32  is 
8,  and  7  times  8  is  56.  Therefore  f  of  3  times  12  is  ±  of  56. 

6.  f  of  3  times  12  is  how  many  sevenths  of  56  ? 
As  many  sevenths  of  56  as  %  of  56  is  contained  times 

in  8  times  i  of  3  times  12.  3  times  12  is  36,  i  of  36  is 
4,  and  8  times  4  is  32  ;  ^  of  5G  is  8,  and  8  is  contained 
in  32,  4  times.  Therefore  f  of  3  times  12  is  4  of  56. 

7.  |  of  3  times  12  is  4  times  what  part  of  56  ? 
Such  a  part  of  56   as  56   is  contained  times  in  \  of  8 

times  l  of  3  times  12  ;  3  times  12  is  36  ;  £  of  36  is  4, 
and  8  times  4  is  32  ;  \  of  32  is  8,  and  56  is  contained  in 
8,  -%  or  \  times.  Therefore  |  of  3  times  12  is  4  times 
4,  or  4,  of  56. 

71.     1.  -f  of  35  is  f  of  how  many  thirds  of  18  ? 

Expressed  by  signs  on  the  blackboard  thus  :  — 
4x35  =  §X3  x!8? 

Of  as  many  thirds  of  1  8  as  ^  of  1  8  is  contained  times 
in  9  times  i  of  4  times  4  of  35  ;  i  of  35  is  5,  and  4  times 
5  is  20  ;  |  of  20  is  4,  and  9  times  4  is  36  ;  |  of  18  is  6, 
and  6  is  contained  in  36,  6  times.  Therefore  -$  of  35  is 
|  of  6  thirds  of  18. 

2.     4  of  35  is  f  of  f  of  what  number  ? 


4  of  35  is  4  of  TJ  of  3  times  A  of  9  times  •?-  of  4  times 

I  J  O  U  U 


172  APPENDIX. 

4  of  35  ;  4  of  35  is  5,  and  4  times  5  is  20  ;  £  of  20  is  4, 
and  9  times  4  is  3G  ;  £  of  30  is  6,  and  3  times  6  is  18. 
Therefore  }  of  35  is  $  of  |  of  18. 

3.  A  of  35  is  f  of  6  times  what  part  of  18  ? 

fx35=f  x*xl8'? 

|  of  35  is  |  of  6  times  such  a  part  of  18  as  18  is  con- 
tained times  in  J  of  9  times  -I  of  4  times  4  of  35.  4  °* 
35  is  5,  and  4  times  5  is  20  ;  -!-  of  20  is  4,  and  9  times  4 
is  36  ;  J  of  36  is  6,  and  1  8  is  comaim-d  in  6,  7fig  or  -^  times. 
Therefore  $  of  35  is  §  of  6  times  •?,  or  «,  of  18. 

4.  A  of  35  is  how  many  ninths  of  f  of  18  ? 

4  x35  —  -gx  g  x  18? 

;*  of  35  is  as  many  ninths  of  {j  of  18  as  -J  of  6  times  ^ 
of  18  is  contained  times  in  4  times  4  °f  35.  4  °f  35  ^s 
5,  and  4  times  5  is  20  ;  J  of  18  is  6,  and  6  times  6  is  36  ; 
i  of  36  is  4,  and  4  is  contained  in  20,  5  times.  There- 
fore 4  of  35  is  §  of  |  of  18. 

5.  4  of  35  is  5  times  what  part  of  f  of  18  ? 

f*35=*xf  Xl8? 

%  of  35  is  5  times  such  a  part  of  |  of  18  as  6  times  J 
of  18  is  contained  times  in  £  of  4  times  4  of  35.  4  °^ 
35  is  5,  and  4  times  5  is  20  ;  'i  of  20  is  4  ;  -J  of  18  is  6, 
and  6  times  6,  is  36  ;  36  is  contained  in  4,  ^  or  £  times. 
Therefore  |  of  35  is  5  times  ^,  or  f,  of  |  of  18. 

6.  f  of  f  of  18  is  4  of  what  number  ? 


$  of  |  of  18  is  4  Of  7  times  \  of  5  times  £  of  6  times 
^  of  18  ;  I  of  18  is  6,  and  6  times  6  is  36  ;  l  of  36  is  c; 
and  5  times  4  is  20  ;  \  of  20  is  5,  and  7  times  5  is  3&, 
Therefore  f  of  |  of  18  is  |  of  35. 

7.     |  of  f  of  18  is  how  many  sevenths  of  35  ? 
§x|  x!8=:7x35  ? 

f  of  |  of  18  is  as  many  sevenths  of  35  as  4  of  35  is 
contained  times  in  5  times  ^  of  6  times  \  of  18  ;  \  of 
18  is  6,  and  6  times  6  is  36  ;  ^  of  36  is  4,  and  5  times  4 


APPENDIX.  173 

is  20  ;  4  of  35   is  5,  and  5  is  contained  in  20,  4  times. 
Therefore  f  of  |  of  18  is  |  of  35. 

8.     f  of  f  of  18  is  4  times  what  part  of  35  ? 
§  x|  x  18=A x  35? 

|  of  |  of  18  is  4  times  such  a  part  of  35  as  35  is  con- 
tained times  in  ]  of  5  times  i  of  6  times  j  of  18.  -J  of 
18  is  6,  and  6  times  6  is  36  ;  ^  of  36  is  4,  and  5  times  4 
is  20 ;  -j  of  20  is  5,  and  35  is  contained  in  5,  -/-  or  4 
times.  Therefore  f  of  1 1  of  4 8  is  4  times  4,  or  $,  of  35. 


72.     1.   |  of  36  is  A  of  how  many  times  f  of  42  ? 

Of  as  many  times  f  of  42  as  2  times  4  of  42  is  con- 
tained tinier  in  9  times  \  of  4  times  ]  of  36  ;  -J  °f  36  is  !?» 
and  4  times  32  is  48  ;  j  of  48  is  12,  and  9  times  12  is 
108  ;  4  of  42  is  6,  and  2  times  6  is  12,  and  12  is  con- 
tained in  108,  9  times.  Therefore  |  Of  36  is  |  of  9  times 
§  of  42. 

2.  f  of  36  is  f  of  9  times  f  of  what  number  ? 

-|  of  36  is  4  of  9  times  f  of  7  times  £  of  £  of  9  times  | 
of  4  times  \ of  36  ;  -J-  of  36  is  12,  and  4  times  12  is  48  ;  \  of 
48  is  12,  and  9  times  12  is  108  ;  lot*  108  is  12,  ^  of  12  is  6, 
and  7  times  6  is  42.  Therefore  |  of  36  is  |  of  9  times  $ 
of  42. 

3.  f  of  36  is  f  of  9  times  how  many  sevenths  of  42  ? 

|  of  36  is  ^  of  9  times  as  many  sevenths  of  42  as  4  of 
42  is  contained  times  in  -J  of  9  times  |  of  4  times  J-  of  36  ; 
\  of  36  is  12,  and  4  times  12  is  48 ;  |  of  48  is  12,  9  times 
12  is  108  ;  1  of  108  is  12  ;  4  of  42  is  6,  and  6  is  con- 
tained in  12,  2  times.  Therefore  -£  of  36  is  4  of  9  times 
f  of  42. 

4.  |  of  36  is  |  of  9  times  2  times  what  part  of  42  ? 

|  of  36  is  |  of  9  times  2  times  such  a  part  of  42  as  42  is 
contained  times  in  \  of  \  of  9  times  |  of  4  times  |  of  36  ; 
\  of  36  is  12,  and  4  times  12  is  48 ;  \  of  48  is  12,  and  9 
times  12  is  108 ;  £  of  108  is  12,  and  -A  of  12  is  6 ;  42  is 


174  APPENDIX. 

contained  in  6,  {\2  or  I  times.  Therefore  -j  of  36  is  £  of 
9  tunes  2  times  ,1,  or  r,  of  42. 

5.  f  of  36  is  how  many  ninths  of  9  times  f  of  42  ? 
•J  of  3G  is  :is  many  ttint/ts  of  9  times  -ij  of  42,  ns  -I  of 

9  times  2  times  j  of  42  is  contained  times  in  4  times  -* 
of  36  ;  *  of  36  is  12,  and  4  times  12  is  48  ;  -\  of  42  is 
6,  and  2  times  r>  is  12  ;  9  times  12  is  108,  and  ^  of  108  is 
12  ;  12  is  contained  in  48,  4  times.  Therefore  J  of  30  is 
$  of  9  times  •  of  42. 

6.  |  of  36  is  4  times  what  part  of  9  times  f  of  42  ? 

>j  of  36  is  4  times  such  a  part  of  9  times  ~  of  42,  as 
9  times  2  times  1  of  42  is  contained  times  in  |  of  4  times  .', 
of  30  ;  J  of  36  is  J2,  and  4  times  12  is  48  ;  :J  of  48  is  12  ; 
4  of  42  is  6,  2  times  (>  is  12,  and  9  times  12  is  108; 
108  is  contained  in  12,  /  r\  or  .',  times.  Therefore -3  of 
36  is  4  times,  J  or  £,  of  9  times  -5j  of  42. 

7.  |  of  9  times  f  of  42  is  -J-  of  what  number  ? 

4  of  9  times  ~  of  42  is  -jj  of  3  times  |  of  4  times  J  rf  9 
times  2  times  ,}  of  42.  4  of  42  is  6,  2  times  6  is  12,  and 
<)  times  12  is  108  ;  ^  of  108  is  12,  and  4  times  12  is  48  ; 
]  of  48  is  12,  and  3  times  12  is  36.  Therefore  £  of  9 
times  §  of  42  is  :j  of  36. 

8.  A  of  9  times  f  of  42  is  how  many  thirds  of  36  ? 

4  of  9  times  f  of  42  is  as  many  thirds  of  36,  as  {  of 
36  is  contained  times  in  4  times  J  of  9  times  2  times  ^ 
of  42;  *  of  42  is  6,  2  times  6  is  12,  and  9  times  12  is 
108  ;  l  of  108  is  12,  and  4  times  12  is  48  ;  |  of  36  is  12, 
and  12  is  contained  in  48,  4  times.  Therefore  |  of  9 
times  f  of  42  is  -J  of  36. 

9.  f  of  9  times  f  of  42  is  4  times  what  part  of  36  ? 

^  of  9  times  i  of  42  is  4  times  such  part  of  36  as  36  is 
contained  times  in  |  of  4  times  ^  of  9  times  2  times  4  of 
42  ;  4  of  42  is  6,  2  times  6  is  12,  and  9  times  12  is  108  ; 
l  of  108  is  12,  and  4  times  12  is  48  ;  \  of  48  is  12,  and 
36  is  contained  in  12,  ||  or  ^  times.  Therefore  ^  of  9 
times  §  of  42  is  4  times,  ^  or  |,  of  36. 


INTELLECTUAL    ARITHMETIC. 


175 


MULTIPLICATION   TABLE. 

Once 

1 

2 

3 

4 

5 

0 

Twice 

are         2 

are         4 

are         6 

are     A8 

are       10 

are       12 

Jptimes 

are        3 

are        6 

are         9 

are       12 

are       15 

are       18 

•^tinies 

are        4 

are        8 

are       12 

are    .  16 

are       20 

are       24 

5  times 

are        5 

are       10 

are       15 

are       20 

are       25 

are       30 

6  times 

are         6 

are       12 

are       18 

are       24 

are      30 

are       36 

7  times 

are        7 

are       14 

are       21 

are       23 

are       35 

are       42 

8  times 

are         8 

are       16 

are       24 

are       32     are       40 

are       48 

9  times 

are        9 

are       18     are       27 

are       36     are       45 

are       54 

10  times 

are       10 

are       20 
are       2-f 

are       30 

are       40     are       50 

are       60 

11  times 

are       11 

are       33 
"are       3lT 

are       44     are       55 

are       66 

12  times 

are       1-2 

are       24 

are       48 

are       60 

are       72 

Once 

7 

8 

9 

10 

11 

12 

Twice 

are       14 

are       16 

are       18 

are       20 

are       22 

are       24 

3  times 

are       21 

are       24 

are       27 

are       30 

are       33 

are       36 

4  times 

are       28 

are       32 

are       36 

are       40 

are       44 

are       48 

5  times 

are       35 

are       40 
are       48 

are       45 

are       50 

are       55 

are       CO 

6  times 

are       42 

are       54 

are       60 

are       66 

are       72 

7  times 

are       49 

are       5o 

are       63 

are       70 

are       77 

are       84 

8  times 

are       56 

are       64 

are       72 

are       80 

are       88 

are       i)6 

9  times 

are       63 

are       72 

are       81 

are       90 

are       99 

are     108 

10  times 

are       70 

are       80 

are       90 

are     100 

are     110 

are     120 

11  times 

are       77 

are       88 

are       99 

are     110 

ai-e      121 

are     132 

.1:3  times 

are       84 

are       96 

are     108 

are     120 

are     132 

are     144 

1 

2 

3 

4 

5 

6 

13  times 

are       13 

are       26 

are       39 

are      52 

are       66 

are       78 

14  times 

are       14 

are       28 

are       42 

are       56 

are       70 

are       84 

15  times 

are       15 

are       30 

are       45 

are       60 

are       75 

are       90 

16  times 

are       16 

are       32 

are       48 

are       64 

are       80 

are       96 

17  times 

are       17 

are       34 

are       51 

are       68     are       85 

are     102 

18  times 

are       16     are       36 

are       54 

are       72     are       90     are     108 

19  times 

are       19     are       38 

are       57 

are       76     are       95     are     114 

20  times 

are       20     are       40  \  are       60     are       80     are     100     are     12J 

21  times 

are       21     are       42  i  are       63 

are       84     are     105     are     Iv'J 

22  times     arc       22     are       44     are       66 

are       88     are     110     are     132 

23  times     are       23     are       46 

are      69 

are       92     are     115     are     138 

24  times    are       24  !  are       48 

are       72     are       96  1  are     120     are     144 

25  times    are      25  ,  are      50  ,  are      75  j  are     100  j  are     125  ,  are     150 

176 


INTELLECTUAL   ARITHMETIC. 


7 

8 

0 

10 

11 

12 

13  times 

are       91 

are     104 

are     117 

are     130 

are     143 

are     156 

14  times 

are      98 

are     112 

are     126 

are     140 

are     154 

are     168 

15  times 

are     105 

are     120 

are     135 

are     150 

are     165 

are     180 

16  times 

are     112 

are     12d 

are     144 

are     160 

are     176 

are     192 

17  times 

are     119 

are     136 

are     153 

are     17J 

are     187 

are     204 

18  times 

are     126 

are     144 

are     162 

are     180 

are     198 

are     216 

19  times 

are     133 

are     152 

are     171 

are     190 

are     209 

are     228 

20  times 

are     140 

are     160 

are     180 

are     200 

are     220 

are     240 

21  times 

are     147 

are     168 

are     189 

are     210 

are     231 

are     252 

22  times 

are     154 

are     176 

are     198 

are     220 

are     242 

are     264 

23  times 

are     161 

are     184 

are     207 

are     230 

are     253 

are     276 

24  times 

are     168 

are     192 

are     216 

are     240 

are     264 

are     288 

25  times 

are     17o 

are     200 

are     225 

are     250 

are     275 

are     300 

13 

14 

15 

16 

17 

18 

13  times 

are     169 

are     182 

are     195 

are     208 

are     22J 

are     234 

14  times 

are     182 

are     196 

are     210 

are     224 

aie     238 

are     252 

15  times 

are     195 

are     210 

are     225 

are     240 

are     255 

are     270 

16  times 

are     208 

are     224 

are     240 

are     256 

are     272 

are     288 

17  times 

are     221 

are     238 

are     255 

are     272 

are     289 

are     306 

18  times 

are     234 

are     252 

are     270 

are     288 

are     306 

are     324 

19  times 

are     247 

are     266 

are     285 

are     304 

are     323 

are     342 

20  times 

are    260 

are     280 

are     300 

are     320 

are     340 

are     360 

21  times 

are     273 

are     294 

are     315 

are     336 

are     357 

are     378 

22  times 

are     286 

are     308 

are     330 

are     352 

are     374 

are     396 

23  times 

are     299 

are     322 

are     345 

are     368 

are     391 

are     414 

24  times 

are     312 

are     336 

are     360 

are     384 

are     408 

are     432 

25  tunes 

are     325 

are     350 

are     375 

are     400 

are     425 

are     450 

19 

20 

21 

22 

23 

24 

13  times 

are     247 

are     260 

are     273 

are     286 

are     299 

are     312 

14  times 

are     266 

are     280 

are     294 

are     308 

are     322 

are     336 

15  times 

are     285 

are     30) 

are     315 

are     330 

are     345 

are     360 

16  tunes 

are     304 

are     320 

are     336 

are     352 

are     368 

are     384 

17  times 

are     323 

are     340 

are     357 

are     374 

are     391 

are     408 

18  times 

are     342 

are     360 

are     378 

are     396 

are     414 

are     432 

19  times 

are     361 

are     380 

are     399 

are     418 

are     437 

are     456 

20  times 

are     380 

are     400 

are     420 

are     440 

are     460 

are     480 

21  times 

are     399 

are     420 

are     441 

are     462 

are     483 

are     504 

22  times 

are     418 

are     440 

are     462 

are     484 

are     506 

are     528 

23  times 

are     437 

are     4  0 

are     483 

are     506 

are     529 

are     552 

24  times 

are     456 

are     480 

are     504 

are     528 

are     552 

are     576 

25  times 

are     475 

are     500 

are     525 

are     550 

are     575 

are     600 

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